Question

Let $N$ be a positive integer that ends in $9$, what are all the possibilities for the last two digits of $n^{10}$?

score 47 · Answer 1 · 2026-04-12 03:34:34

Let $N$ be a positive integer that ends in $9$, what are all the possibilities for the last two digits of $n^{10}$?

score 69 · Answer 2 · 2026-03-26 12:37:32

69

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If $a_n = 2^{n-1}(2^{n-1}-1)a_{n-1}$, $a_1=1$, show that $n \mid a_n$

Published on 26 Mar 2026 - 12:37

score 105 · Answer 3 · 2026-04-11 12:57:04

105

Views

Basic theorem in Polynomial Congruence

Published on 11 Apr 2026 - 12:57

score 597 · Answer 4 · 2026-04-01 06:01:57

597

Views

$5$-digit number from $0-9$

Published on 01 Apr 2026 - 6:01

score 812 · Answer 5 · 2026-04-10 08:43:41

812

Views

Proof of the cube root trick

Published on 10 Apr 2026 - 8:43

score 865 · Answer 6 · 2026-04-13 15:14:48

865

Views

What is the probability of that a number in the set of natural numbers is divisible by $3$ but not by $9$?

Published on 13 Apr 2026 - 15:14

score 627 · Answer 7 · 2026-03-26 10:45:07

627

Views

2 proofs Regarding Elliptic curves

Published on 26 Mar 2026 - 10:45

score 115 · Answer 8 · 2026-04-13 02:08:26

115

Views

Elementary Number Theory: Solving Quadratic Conguences

Published on 13 Apr 2026 - 2:08

score 1.4k · Answer 9 · 2026-04-13 08:40:41

1.4k

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How many $4$ digit numbers have a digit sum of $11$?

Published on 13 Apr 2026 - 8:40

score 218 · Answer 10 · 2018-03-10 23:39:25

218

Views

Prove that every prime factor of $12x^2+1$ has the form $6n+1$

Published on 10 Mar 2018 - 23:39

score 240 · Answer 11 · 2026-03-25 03:07:05

240

Views

When is $2^{2n+2}+2^{m+2}+1$ a perfect square?

Published on 25 Mar 2026 - 3:07

score 58 · Answer 12 · 2026-03-25 03:01:40

58

Views

Proving $2^n=2^m=k$ in $2^{2n}+2^m=k^2+k$

Published on 25 Mar 2026 - 3:01

score 333 · Answer 13 · 2026-03-26 01:06:46

333

Views

Why do Sylvester numbers, when reduced modulo $864$, form an arithmetic progression $7, 43, 79, 115, 151, 187, 223, \ldots$?

Published on 26 Mar 2026 - 1:06

score 45 · Answer 14 · 2026-03-28 21:06:48

45

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Find a $N \in I \ni \left|\frac{2n}{n+3} - 3\right| < \frac{1}{5}\,\forall\,n\geq N$

Published on 28 Mar 2026 - 21:06

score 222 · Answer 15 · 2026-03-25 04:44:23

222

Views

An approximation for $1\leq n\leq N$ of the number of solutions of $2^{\pi(n)}\equiv 1\text{ mod }n$, where $\pi(x)$ is the prime-counting function

Published on 25 Mar 2026 - 4:44

List Question

Let $N$ be a positive integer that ends in $9$, what are all the possibilities for the last two digits of $n^{10}$?

If $a_n = 2^{n-1}(2^{n-1}-1)a_{n-1}$, $a_1=1$, show that $n \mid a_n$

Basic theorem in Polynomial Congruence

$5$-digit number from $0-9$

Proof of the cube root trick

What is the probability of that a number in the set of natural numbers is divisible by $3$ but not by $9$?

2 proofs Regarding Elliptic curves

Elementary Number Theory: Solving Quadratic Conguences

How many $4$ digit numbers have a digit sum of $11$?

Prove that every prime factor of $12x^2+1$ has the form $6n+1$

When is $2^{2n+2}+2^{m+2}+1$ a perfect square?

Proving $2^n=2^m=k$ in $2^{2n}+2^m=k^2+k$

Why do Sylvester numbers, when reduced modulo $864$, form an arithmetic progression $7, 43, 79, 115, 151, 187, 223, \ldots$?

Find a $N \in I \ni \left|\frac{2n}{n+3} - 3\right| < \frac{1}{5}\,\forall\,n\geq N$

An approximation for $1\leq n\leq N$ of the number of solutions of $2^{\pi(n)}\equiv 1\text{ mod }n$, where $\pi(x)$ is the prime-counting function

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