Question

Conjecture: $N=x_1^2+x_2^2-y^3$ has integer solutions for all $N$, with $x_1>0$,$x_2>0$ and $y>0$

score 139 · Answer 1 · 2026-04-07 04:31:44

139

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Conjecture: $N=x_1^2+x_2^2-y^3$ has integer solutions for all $N$, with $x_1>0$,$x_2>0$ and $y>0$

Published on 07 Apr 2026 - 4:31

score 56 · Answer 2 · 2026-04-07 02:11:38

56

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Digit counts in the multiples of $n$

Published on 07 Apr 2026 - 2:11

score 59 · Answer 3 · 2026-04-07 03:57:30

59

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Prove that if $a|b_1b_2$, $a|c_1c_2$ and $a|b_1c_1+b_2c_2$, then $a|b_1c_1$ and $a|b_2c_2$

Published on 07 Apr 2026 - 3:57

score 71 · Answer 4 · 2026-04-07 09:38:51

71

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Proving $\forall n \in \mathbb Z, n>0, \;\exists x_n\in \mathbb Z$ such that $x_n^2 \equiv 14 \pmod {5^n}$

Published on 07 Apr 2026 - 9:38

score 1.4k · Answer 5 · 2026-04-06 17:20:16

1.4k

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Alternating series of primes

Published on 06 Apr 2026 - 17:20

score 47 · Answer 6 · 2026-04-07 01:15:03

47

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Given $b\mid (ac-1)$ show that $(a,b) = 1$

Published on 07 Apr 2026 - 1:15

score 200 · Answer 7 · 2026-04-07 02:43:55

200

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How one should approach a problem involving alteration in digits of integers

Published on 07 Apr 2026 - 2:43

score 114 · Answer 8 · 2026-04-07 13:04:01

114

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Proof for : if $((a \mid b),$ & $(a \nmid c))$, then $b\nmid c.$

Published on 07 Apr 2026 - 13:04

score 145 · Answer 9 · 2026-04-06 23:53:48

145

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The Chinese hypothesis revisited

Published on 06 Apr 2026 - 23:53

score 119 · Answer 10 · 2026-04-07 14:43:45

119

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How many times do a couple of bells ring close enough that they are heard as one?

Published on 07 Apr 2026 - 14:43

score 128 · Answer 11 · 2026-04-07 10:36:02

128

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Formulaic representation of the lowest form of the denominator of a rational number

Published on 07 Apr 2026 - 10:36

score 148 · Answer 12 · 2026-04-06 20:10:08

148

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Find the formula for $1 + 4 + 7 +\ldots+ (3n - 2)$ and verify the formula by induction

Published on 06 Apr 2026 - 20:10

score 40 · Answer 13 · 2026-04-07 09:24:27

40

Views

How to apply constraints on a number

Published on 07 Apr 2026 - 9:24

score 157 · Answer 14 · 2026-04-07 11:44:11

157

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Polynomial p(a)=1, why does it have at most 2 integer roots?

Published on 07 Apr 2026 - 11:44

score 1.6k · Answer 15 · 2026-04-09 02:07:17

1.6k

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Existence of Solution to Generalized Pell's Equation

Published on 09 Apr 2026 - 2:07

List Question

Conjecture: $N=x_1^2+x_2^2-y^3$ has integer solutions for all $N$, with $x_1>0$,$x_2>0$ and $y>0$

Digit counts in the multiples of $n$

Prove that if $a|b_1b_2$, $a|c_1c_2$ and $a|b_1c_1+b_2c_2$, then $a|b_1c_1$ and $a|b_2c_2$

Proving $\forall n \in \mathbb Z, n>0, \;\exists x_n\in \mathbb Z$ such that $x_n^2 \equiv 14 \pmod {5^n}$

Alternating series of primes

Given $b\mid (ac-1)$ show that $(a,b) = 1$

How one should approach a problem involving alteration in digits of integers

Proof for : if $((a \mid b),$ & $(a \nmid c))$, then $b\nmid c.$

The Chinese hypothesis revisited

How many times do a couple of bells ring close enough that they are heard as one?

Formulaic representation of the lowest form of the denominator of a rational number

Find the formula for $1 + 4 + 7 +\ldots+ (3n - 2)$ and verify the formula by induction

How to apply constraints on a number

Polynomial p(a)=1, why does it have at most 2 integer roots?

Existence of Solution to Generalized Pell's Equation

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