Question

How to simplify a fraction that has matrix

score 205 · Answer 1 · 2026-04-03 04:50:27

205

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How to simplify a fraction that has matrix

Published on 03 Apr 2026 - 4:50

score 296 · Answer 2 · 2020-06-23 15:31:29

296

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For how many natural numbers(<=100) is $1111^n +2222^n+3333^n+4444^n$ divisible by 10?

Published on 23 Jun 2020 - 15:31

score 42 · Answer 3 · 2026-03-30 17:09:59

42

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If $\gcd(a,p)=1$, $p$ is prime, prove that there are $1\le x, y\le [\sqrt p]$ that $ax≡y\pmod p$ or $ax≡-y\pmod p$

Published on 30 Mar 2026 - 17:09

score 161 · Answer 4 · 2020-06-26 02:18:00

161

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Relationship between primes, right triangles and homogeneous polynomials

Published on 26 Jun 2020 - 2:18

score 65 · Answer 5 · 2020-06-27 06:08:10

65

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Pythagorean triplets which satisfy the prime counting function $\omega(n)$

Published on 27 Jun 2020 - 6:08

score 97 · Answer 6 · 2020-06-27 20:04:09

97

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Are there infinitely many primes which are the sum of the two sides of a right triangle?

Published on 27 Jun 2020 - 20:04

score 135 · Answer 7 · 2020-06-28 20:21:18

135

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Is this an acceptable proof for If $d^{2}\mid a^{2}$ , then $d\mid a$?

Published on 28 Jun 2020 - 20:21

score 57 · Answer 8 · 2020-06-30 07:11:15

57

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Prove the statements.

Published on 30 Jun 2020 - 7:11

score 144 · Answer 9 · 2020-06-30 12:56:15

144

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Prove by mathematical induction, that $81\times 3^{2n} - 2^{2n}$ is divisible by $5$ where $n \in \mathbb{Z}^+$

Published on 30 Jun 2020 - 12:56

score 39 · Answer 10 · 2026-03-30 14:41:16

39

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Question on binomial expansion - divisibility by power of divisor

Published on 30 Mar 2026 - 14:41

score 52 · Answer 11 · 2026-03-25 14:26:52

52

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On an equation that involves the number-of-divisors function and the formula for a sequence of figurate numbers

Published on 25 Mar 2026 - 14:26

score 110 · Answer 12 · 2026-03-28 01:08:34

110

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If $ 1+ \frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}=\frac{A}{B}$ where $A$ and $B$ are coprime positive integers, then $5\nmid A$ and $5\nmid B$.

Published on 28 Mar 2026 - 1:08

score 90 · Answer 13 · 2020-07-04 02:25:10

90

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Prove that $q$ divides (${}_q \mathrm{C}_x$) where $q$ is an odd prime and $x \in \Bbb{Z}$ is such that $1\lt x \lt q$.

Published on 04 Jul 2020 - 2:25

score 42 · Answer 14 · 2026-03-29 15:33:20

42

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How many numbers between 1 and 1,000 (both inclusive) are divisible by at least one of the prime between 1 to 50? How can I find this?

Published on 29 Mar 2026 - 15:33

score 128 · Answer 15 · 2026-03-29 12:12:03

128

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Show that for all $n$ there exist some $n$-digit number with no $0$ in it whose digit sum divides it.

Published on 29 Mar 2026 - 12:12

List Question

How to simplify a fraction that has matrix

For how many natural numbers(<=100) is $1111^n +2222^n+3333^n+4444^n$ divisible by 10?

If $\gcd(a,p)=1$, $p$ is prime, prove that there are $1\le x, y\le [\sqrt p]$ that $ax≡y\pmod p$ or $ax≡-y\pmod p$

Relationship between primes, right triangles and homogeneous polynomials

Pythagorean triplets which satisfy the prime counting function $\omega(n)$

Are there infinitely many primes which are the sum of the two sides of a right triangle?

Is this an acceptable proof for If $d^{2}\mid a^{2}$ , then $d\mid a$?

Prove the statements.

Prove by mathematical induction, that $81\times 3^{2n} - 2^{2n}$ is divisible by $5$ where $n \in \mathbb{Z}^+$

Question on binomial expansion - divisibility by power of divisor

On an equation that involves the number-of-divisors function and the formula for a sequence of figurate numbers

If $ 1+ \frac{1}{2}+\frac{1}{3}+.....+\frac{1}{100}=\frac{A}{B}$ where $A$ and $B$ are coprime positive integers, then $5\nmid A$ and $5\nmid B$.

Prove that $q$ divides (${}_q \mathrm{C}_x$) where $q$ is an odd prime and $x \in \Bbb{Z}$ is such that $1\lt x \lt q$.

How many numbers between 1 and 1,000 (both inclusive) are divisible by at least one of the prime between 1 to 50? How can I find this?

Show that for all $n$ there exist some $n$-digit number with no $0$ in it whose digit sum divides it.

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