List questions from divisibility

Published on 15 Dec 2019 - 20:17

64

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Proving a | ($b^2$ + $c^2$) if a | b and a | c

Published on 16 Dec 2019 - 2:57

127

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Prove that $11^{10^3} \equiv 1 \pmod{10^4}$

Published on 17 Dec 2019 - 21:03

717

Views

I proved something wrong. If a and b are irrational proof that a + b is irrational or rational.

Published on 26 Mar 2026 - 19:18

154

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Prove that $3^k+6k-1$ is divisible by 4 using modular arithmetic.

Published on 18 Dec 2019 - 17:59

32

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Proportional division of a number (given percentages)

Published on 19 Dec 2019 - 17:33

125

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If two side of a Pythagorean triangle are primes then the third side has at least $4$ distinct prime factors.

Published on 20 Dec 2019 - 4:52

229

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Does every solution of $x^2 = y^2 - z^2$ where $y$ and $z$ are primes $> 5000$ has a prime factor greater than $17$.

Published on 29 Mar 2026 - 16:39

47

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Help with Proof Involving Sets

Published on 22 Dec 2019 - 21:31

62

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Determine the remainder in the division of $ a_ {2019} $

Published on 30 Mar 2026 - 6:11

860

Views

AMC 2017 junior question

Published on 23 Dec 2019 - 9:07

116

Views

Clever way to find zero remainder with decreasing divisor

Published on 02 Apr 2026 - 9:01

125

Views

Remainder Theorem Question: Deduce the Polynomial Given the Remainder

Published on 23 Dec 2019 - 20:18

56

Views

Divisibility of perfect numbers

Published on 26 Mar 2026 - 2:50

977

Views

Is there a prime every year if YYYYMMDD is treated as a base-$10$ number?

Published on 27 Dec 2019 - 5:13

List Question

Determine the remainder in the division of $ a_ {2019} $ by 2019

Proving a | ($b^2$ + $c^2$) if a | b and a | c

Prove that $11^{10^3} \equiv 1 \pmod{10^4}$

I proved something wrong. If a and b are irrational proof that a + b is irrational or rational.

Prove that $3^k+6k-1$ is divisible by 4 using modular arithmetic.

Proportional division of a number (given percentages)

If two side of a Pythagorean triangle are primes then the third side has at least $4$ distinct prime factors.

Does every solution of $x^2 = y^2 - z^2$ where $y$ and $z$ are primes $> 5000$ has a prime factor greater than $17$.

Help with Proof Involving Sets

Determine the remainder in the division of $ a_ {2019} $

AMC 2017 junior question

Clever way to find zero remainder with decreasing divisor

Remainder Theorem Question: Deduce the Polynomial Given the Remainder

Divisibility of perfect numbers

Is there a prime every year if YYYYMMDD is treated as a base-$10$ number?

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