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Number TheoryQuestion and Answers: Page 1

Question Number 213756 Answers: 1 Comments: 0

Question Number 213663 Answers: 1 Comments: 0

Given a,b,c is natural numbers such that (a−b)(b−c)(c−a)=a+b+c. find min value of a+b+c

$$\:\:\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{is}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{b}−\mathrm{c}\right)\left(\mathrm{c}−\mathrm{a}\right)=\mathrm{a}+\mathrm{b}+\mathrm{c}. \\ $$$$\:\:\mathrm{find}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}+\mathrm{b}+\mathrm{c}\: \\ $$

Question Number 212999 Answers: 1 Comments: 0

Find the number of non zero integer solution (x,y) to the equation ((15)/(x^2 y)) + (3/(xy)) − (2/x) = 2

$$\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{integer}\: \\ $$$$\:\mathrm{solution}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\:\:\:\frac{\mathrm{15}}{\mathrm{x}^{\mathrm{2}} \mathrm{y}}\:+\:\frac{\mathrm{3}}{\mathrm{xy}}\:−\:\frac{\mathrm{2}}{\mathrm{x}}\:=\:\mathrm{2}\: \\ $$

Question Number 212242 Answers: 0 Comments: 7

Help

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Question Number 212201 Answers: 1 Comments: 0

find the last two digits of 9^9^9 ?

$$\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{two}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{9}^{\mathrm{9}^{\mathrm{9}} } \:? \\ $$

Question Number 211943 Answers: 2 Comments: 1

2^(m−1) =1+mn m, n ∈Z

$$\mathrm{2}^{{m}−\mathrm{1}} =\mathrm{1}+{mn} \\ $$$${m},\:{n}\:\in\mathbb{Z} \\ $$

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Question Number 208506 Answers: 2 Comments: 0

What is the smallest number which must added to 9454351626 so that it will become divisible by 11?

Question Number 207713 Answers: 2 Comments: 0

Question Number 207436 Answers: 1 Comments: 2

a, b∈N_+ , ((b+1)/a)+((a+1)/b)∈Z. Prove that (a, b)≤(√(a+b.))

$${a},\:{b}\in\mathbb{N}_{+} ,\:\frac{{b}+\mathrm{1}}{{a}}+\frac{{a}+\mathrm{1}}{{b}}\in\mathbb{Z}.\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\left({a},\:{b}\right)\leqslant\sqrt{{a}+{b}.} \\ $$

Question Number 207423 Answers: 2 Comments: 0

⇃

$$\:\:\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 207060 Answers: 2 Comments: 0

⇃

$$\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 207021 Answers: 1 Comments: 1

If a_(n+1) =2−5a_n and a_4 = −8 prove that a_(43) −a_(30) divisible by 5

$$\:\:{If}\:\:{a}_{{n}+\mathrm{1}} =\mathrm{2}−\mathrm{5}{a}_{{n}} \:{and}\:{a}_{\mathrm{4}} =\:−\mathrm{8} \\ $$$$\:\:{prove}\:{that}\:{a}_{\mathrm{43}} −{a}_{\mathrm{30}} \:{divisible}\:{by}\:\mathrm{5} \\ $$

Question Number 206999 Answers: 3 Comments: 1

Prove that 6^(20) −1 = 0 (mod 7)

$$\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}^{\mathrm{20}} −\mathrm{1}\:=\:\mathrm{0}\:\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$

Question Number 206912 Answers: 3 Comments: 0

Question Number 205922 Answers: 2 Comments: 0

x = 2 (mod 7) x=3 (mod 4) x=?

$$\:\:\:{x}\:=\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right) \\ $$$$\:\:\:{x}=\mathrm{3}\:\left({mod}\:\mathrm{4}\right) \\ $$$$\:\:\:{x}=? \\ $$

Question Number 204568 Answers: 1 Comments: 0

how to convert 31230 in base 60? pls help

$$\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{convert}}\:\mathrm{31230}\:\boldsymbol{{in}}\:\boldsymbol{{base}}\:\mathrm{60}? \\ $$$$\boldsymbol{{pls}}\:\boldsymbol{{help}} \\ $$

Question Number 203509 Answers: 0 Comments: 0

Find the value of: Π_(n=1) ^∞ ((2^n +1)/(2^n −1))

$${Find}\:{the}\:{value}\:{of}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\mathrm{2}^{{n}} +\mathrm{1}}{\mathrm{2}^{{n}} −\mathrm{1}} \\ $$

Question Number 203146 Answers: 1 Comments: 0

Determine ab^(−) (a>b) such that( ab^(−) +ba^(−) ) and (ab^(−) −ba^(−) ) are both perfect squares.

$$\mathcal{D}{etermine}\:\overline {{ab}}\:\left({a}>{b}\right)\:{such}\:{that}\left(\:\overline {{ab}}+\overline {{ba}}\right)\: \\ $$$${and}\:\left(\overline {{ab}}−\overline {{ba}}\right)\:{are}\:{both}\:{perfect}\:{squares}. \\ $$

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