Question and Answers Forum

All Questions   Topic List

Number TheoryQuestion and Answers: Page 3

Question Number 192909    Answers: 0   Comments: 0

let P(x) is polinomial with integer coefficient s.t P(6)P(38)P(57)+19 is divided by 114. P(-13)=479 and P≥0 what is minimum value of P(0)?

$$\: \\ $$$$\:{let}\:{P}\left({x}\right)\:{is}\:{polinomial}\:{with}\:{integer} \\ $$$$\:{coefficient}\:{s}.{t}\:{P}\left(\mathrm{6}\right){P}\left(\mathrm{38}\right){P}\left(\mathrm{57}\right)+\mathrm{19}\:{is} \\ $$$$\:{divided}\:{by}\:\mathrm{114}.\:{P}\left(-\mathrm{13}\right)=\mathrm{479}\:{and}\:{P}\geqslant\mathrm{0} \\ $$$$\:{what}\:{is}\:{minimum}\:{value}\:{of}\:{P}\left(\mathrm{0}\right)? \\ $$$$ \\ $$

Question Number 191889    Answers: 2   Comments: 0

Σ_(n=1) ^k (1/(n^2 +2n)) =?

$$\:\:\:\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{k}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2n}}\:=? \\ $$

Question Number 191862    Answers: 1   Comments: 1

Find the last digit from (2^(400) −2^(320) )(2^(200) +2^(160) )(2^(200) −2^(160) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{from}\: \\ $$$$\:\left(\mathrm{2}^{\mathrm{400}} −\mathrm{2}^{\mathrm{320}} \right)\left(\mathrm{2}^{\mathrm{200}} +\mathrm{2}^{\mathrm{160}} \right)\left(\mathrm{2}^{\mathrm{200}} −\mathrm{2}^{\mathrm{160}} \right) \\ $$

Question Number 191846    Answers: 1   Comments: 0

find the last three digits of 4^2^(42) Mohammed Alwan

$${find}\:{the}\:{last}\:{three}\:{digits} \\ $$$${of}\:\mathrm{4}^{\mathrm{2}^{\mathrm{42}} } \\ $$$${Mohammed}\:{Alwan} \\ $$

Question Number 191710    Answers: 0   Comments: 1

What is the remainder f 149! when divided by 139?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{f}\:\mathrm{149}!\:\mathrm{when}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\mathrm{139}? \\ $$

Question Number 191680    Answers: 1   Comments: 0

Find the remainder of 67! when divided by 7!

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{of}\:\mathrm{67}!\:\mathrm{when}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\mathrm{7}! \\ $$

Question Number 191232    Answers: 1   Comments: 0

If x^2 − y^2 = 2023^(2023) then how many pair of x,y where x, y ∈ N

$$\mathrm{If}\:{x}^{\mathrm{2}} \:−\:{y}^{\mathrm{2}} \:=\:\mathrm{2023}^{\mathrm{2023}} \:\mathrm{then}\:\mathrm{how}\:\mathrm{many}\: \\ $$$$\mathrm{pair}\:\mathrm{of}\:{x},{y}\:{where}\:{x},\:{y}\:\in\:\mathrm{N} \\ $$

Question Number 190568    Answers: 0   Comments: 1

Question Number 190569    Answers: 1   Comments: 0

The number of 4−digit numbers that contain the number 6 and are divisible by 3 is ___

$$\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{4}−\mathrm{digit}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{contain}\:\mathrm{the} \\ $$$$\:\mathrm{number}\:\mathrm{6}\:\mathrm{and}\:\mathrm{are}\:\mathrm{divisible}\: \\ $$$$\:\mathrm{by}\:\mathrm{3}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 190544    Answers: 1   Comments: 1

Given p,q,r,s sre distinc prime numbers such that pq−rs divisible by 30. minimum value of p+q+r+s =?

$$\mathrm{Given}\:\mathrm{p},\mathrm{q},\mathrm{r},\mathrm{s}\:\mathrm{sre}\:\mathrm{distinc}\:\mathrm{prime}\:\mathrm{numbers} \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{pq}−\mathrm{rs}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{30}. \\ $$$$\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}+\mathrm{q}+\mathrm{r}+\mathrm{s}\:=? \\ $$

Question Number 190286    Answers: 1   Comments: 0

Question Number 190285    Answers: 1   Comments: 5

Question Number 189090    Answers: 2   Comments: 0

Question Number 188196    Answers: 3   Comments: 2

(1)solve Diopthantine equation 754x+221y=13 (2) find the number abcd such that 4×(abcd)=dcba

$$\left(\mathrm{1}\right)\mathrm{solve}\:\mathrm{Diopthantine}\:\mathrm{equation} \\ $$$$\:\:\:\:\:\mathrm{754x}+\mathrm{221y}=\mathrm{13} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{abcd}\: \\ $$$$\:\:\:\mathrm{such}\:\mathrm{that}\:\mathrm{4}×\left(\mathrm{abcd}\right)=\mathrm{dcba} \\ $$

Question Number 187300    Answers: 0   Comments: 0

Find the number of integral solutions of (p+q)(q+r)(r+p)=8pqr+2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{solutions}\:\mathrm{of} \\ $$$$\left({p}+{q}\right)\left({q}+{r}\right)\left({r}+{p}\right)=\mathrm{8}{pqr}+\mathrm{2} \\ $$

Question Number 187296    Answers: 0   Comments: 1

Prove that for n≥4, S_n = Σ_(k=1) ^n k^(k!) is never a perfect cube.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{n}\geqslant\mathrm{4},\:\mathrm{S}_{{n}} =\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}^{{k}!} \:\mathrm{is}\:\mathrm{never}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{cube}. \\ $$

Question Number 187213    Answers: 0   Comments: 0

If a,b are co-prime natural numbers satisfying a^2 + b = (a−b)^3 and b+1 is a prime find all possible values of (a, b). Please help me solve this.

$$\mathrm{If}\:{a},{b}\:\mathrm{are}\:\mathrm{co}-\mathrm{prime}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{satisfying} \\ $$$${a}^{\mathrm{2}} \:+\:{b}\:=\:\left({a}−{b}\right)^{\mathrm{3}} \:\mathrm{and}\:{b}+\mathrm{1}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{find}\:\mathrm{all} \\ $$$$\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\left({a},\:{b}\right). \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this}. \\ $$$$ \\ $$

Question Number 183998    Answers: 1   Comments: 1

Find the natural number n such n=7^a ∙17^b a∈N, b∈N and the sum of all its divisors (1 and n included) is 2456.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}}\:{such} \\ $$$$\:\:\:\:\:\:\:{n}=\mathrm{7}^{{a}} \centerdot\mathrm{17}^{{b}} \:\:\:\:\:\:{a}\in\mathbb{N},\:\:\:{b}\in\mathbb{N} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{its}\:\mathrm{divisors}\:\left(\mathrm{1}\:\mathrm{and}\right. \\ $$$$\left.\boldsymbol{\mathrm{n}}\:\mathrm{included}\right)\:\mathrm{is}\:\mathrm{2456}. \\ $$

Question Number 183678    Answers: 0   Comments: 0

find the laplace invesrse for I(s) I(s)=((2000s^2 )/((s^2 +200^2 )(s^2 +400s+2×10^5 )))

$${find}\:{the}\:{laplace}\:{invesrse}\:{for}\:{I}\left({s}\right) \\ $$$${I}\left({s}\right)=\frac{\mathrm{2000}{s}^{\mathrm{2}} }{\left({s}^{\mathrm{2}} +\mathrm{200}^{\mathrm{2}} \right)\left({s}^{\mathrm{2}} +\mathrm{400}{s}+\mathrm{2}×\mathrm{10}^{\mathrm{5}} \right)} \\ $$

Question Number 182199    Answers: 2   Comments: 0

Let S={1, 2, 3, 4, 5, 6, 7} If we multiply atleast 2 numbers from this set with each other, what are the chances of the product to turn out to be divisible by 3?

$${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$

Question Number 182374    Answers: 2   Comments: 1

Question Number 181313    Answers: 2   Comments: 0

Montrer que 3^(2n+1) +2^(n+2) est divisible par 7

$${Montrer}\:{que} \\ $$$$\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{2}^{{n}+\mathrm{2}} \:\:\:{est}\:{divisible}\:{par}\:\mathrm{7} \\ $$

Question Number 180877    Answers: 1   Comments: 1

Q. find the largest value of such that the positive integers a, b > 1 satisfy. a^b .b^a + a^b + b^a = 5329

$$\boldsymbol{\mathrm{Q}}.\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{integers}}\:\:\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}}\:>\:\mathrm{1}\:\boldsymbol{\mathrm{satisfy}}. \\ $$$$\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} .\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:+\:\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{b}}} \:+\:\boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{a}}} \:=\:\mathrm{5329} \\ $$

Question Number 180776    Answers: 2   Comments: 0

Simplify (√((4/( (√2))) + 3))

$${Simplify}\:\:\sqrt{\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}}}\:+\:\mathrm{3}}\: \\ $$$$ \\ $$

Question Number 180746    Answers: 2   Comments: 0

Question Number 180115    Answers: 1   Comments: 0

  Pg 1      Pg 2      Pg 3      Pg 4      Pg 5      Pg 6      Pg 7      Pg 8      Pg 9      Pg 10   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com