Number Theory — Page 1 — Tinkutara Math Forum

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Question 228988

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Question #228610

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a=(dv/dt)=((v−u)/t) a=((v−u)/t) v−u=at v=u+at.....eq(i) 6.Distance(S).it is the how far a body t

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Is there an n>11 such that every digit of 2^n in decimal representation is even?

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(202519)^(2025)

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Question 227080

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2^(2025) ×3^(2025)

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Question 223480

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Question 222974

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Question 222635

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Given the integer k,how to find the incomplete general solution for the non-trivial integer solutions of the Diophantine equation: a^4 +b^4 +ka^2 b^2 =c^4 +d^4 +kc^2 d^2 ,a,b,c,d∈N,k∈Z,gcd(a,b,c,d)=1

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Question 219732

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prove; Π_(n=1) ^∞ (((5n−2)(5n−3))/((5n−1)(5n−4))) = ϕ

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An amazing thing i saw S = 1 + 2 + 3 + 4 + 5 + 6... = 1 + 2(2/2 + 3/2 + 4/2 + 5/2 +6/2....) = 1 + 2(1 + 3/2 + 2 + 5/2 + 3...) = 1 + 2(1+ 2 + 3 ... + 3/2 + 5/2...) = 1 + 2S + 2Σ_(n= 1) ^∞ ((2n + 1)/2) or,S − 2S = 1 + Σ_(n=1) ^∞ 2n + 1 ∴ −S = Σ_(n=0) ^∞ 2n + 1 Sum of all odd numbers! I know the step S−2S = −S is not allowed

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This question is really important Prove or disprove that lim_(n→∞) ((3^n m+3^(n−1) )/2^(⌈(n/2)⌉) ) + (3^(n−1) /2^n ) the limit exists for m ∈ N \B where B = {n ∣ log_2 (n) ∈ N }

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How many ways to arrnge the letters ABCCCDEFG (1) in general . (2) all 3 Cs must be together (3) only 2 Cs must be together (4) no 2 or 3 Cs be together (5) no letter still in its original place .

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a,b,c∈Z^+ and a^2 +b^2 +c^2 +ab+bc+ca=2025 find out all triplets (a,b,c).

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If x∈Z ∧y non-negative integer such that x^2 +10x+23=2^y find out x,y

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Find all two-digit numbers such that when the number is divided by the sum of its digits the quotient is 4 and the remainder is 3.

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Find all integers n> 1 such that n divides 2^(n−1) + 3^(n−1) .

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Prove that for every integer n≥2 the number n^4 + 4^n is composite.

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prove that if an integer n is not divisible by 2 or 3 then n^2 ≡1(mod 24)

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Find all two-digit numbers that are equal to four times the sum of their digits. Solve this using at least two different methods and verify your answers.