Question

Without resorting to induction show that $L_n^2=L_{n+1}L_{n-1}+5(-1)^n$,Where $L_n$ is $n^{th}$ Lucas number.

score 251 · Answer 1 · 2026-04-20 09:31:17

251

Views

Without resorting to induction show that $L_n^2=L_{n+1}L_{n-1}+5(-1)^n$,Where $L_n$ is $n^{th}$ Lucas number.

Published on 20 Apr 2026 - 9:31

score 64 · Answer 2 · 2026-04-17 09:57:24

64

Views

Find integers $\alpha$ and $\beta$ such that $37469\alpha+52464\beta=-11$

Published on 17 Apr 2026 - 9:57

score 262 · Answer 3 · 2026-04-21 10:45:45

262

Views

$N$ square-free $\Rightarrow \exists a \in (\mathbb Z / N\mathbb Z)^{\times}, (\frac{a}{N}) = -1$

Published on 21 Apr 2026 - 10:45

score 271 · Answer 4 · 2026-04-15 00:28:22

271

Views

Find $7^{100} \pmod{167}$ using Fermat's Little Theorem

Published on 15 Apr 2026 - 0:28

score 877 · Answer 5 · 2026-04-17 16:07:24

877

Views

Show $x^2$ + $y^2$ + $z^2$ = $2xyz$ has no non-trivial solutions using infinite descent.

Published on 17 Apr 2026 - 16:07

score 90 · Answer 6 · 2026-04-14 15:55:50

90

Views

Must there exist a number of digits $n$, for which the first $n$ digits of a normal number repeat?

Published on 14 Apr 2026 - 15:55

score 1.3k · Answer 7 · 2026-04-15 10:17:11

1.3k

Views

Prove that a perfect square is not a primitive root modulo $p$ for any prime $p>3$

Published on 15 Apr 2026 - 10:17

score 223 · Answer 8 · 2026-04-16 05:39:28

223

Views

Trying to prove that if $n^2=3q$, then $n=3p$ for $n,p,q \in\mathbb{N}$.

Published on 16 Apr 2026 - 5:39

score 4.5k · Answer 9 · 2026-04-13 08:37:42

4.5k

Views

How do I show that $n$ is prime if and only if $\phi(n) = n − 1$?

Published on 13 Apr 2026 - 8:37

score 137 · Answer 10 · 2026-04-09 10:14:52

137

Views

Which polynomials are "transitive" with respect to $\mathbb{Z}/r\mathbb{Z}$?

Published on 09 Apr 2026 - 10:14

score 348 · Answer 11 · 2026-04-16 10:23:14

348

Views

Show that if $x$ is a primitive root modulo $p^r$, then $x$ is a primitive root modulo $p$

Published on 16 Apr 2026 - 10:23

score 522 · Answer 12 · 2026-04-14 21:26:16

522

Views

Are there infinitely many numbers such that $ \phi(n)=\phi(n-1)+\phi(n-2)$?

Published on 14 Apr 2026 - 21:26

score 5.3k · Answer 13 · 2026-04-16 00:50:46

5.3k

Views

"Find which coin is fake and which is genuine?"-A coin riddle on parity of numbers

Published on 16 Apr 2026 - 0:50

score 131 · Answer 14 · 2026-04-17 14:50:41

131

Views

Solution of the Diophantine Equation $x^2-ay+c=0.$

Published on 17 Apr 2026 - 14:50

score 90 · Answer 15 · 2026-04-17 04:30:26

90

Views

Prove that for every prime number $|\{1\leq x \leq p^2 : p^2 | (x^{p-1}-1) \}|=p-1$

Published on 17 Apr 2026 - 4:30

List Question

Without resorting to induction show that $L_n^2=L_{n+1}L_{n-1}+5(-1)^n$,Where $L_n$ is $n^{th}$ Lucas number.

Find integers $\alpha$ and $\beta$ such that $37469\alpha+52464\beta=-11$

$N$ square-free $\Rightarrow \exists a \in (\mathbb Z / N\mathbb Z)^{\times}, (\frac{a}{N}) = -1$

Find $7^{100} \pmod{167}$ using Fermat's Little Theorem

Show $x^2$ + $y^2$ + $z^2$ = $2xyz$ has no non-trivial solutions using infinite descent.

Must there exist a number of digits $n$, for which the first $n$ digits of a normal number repeat?

Prove that a perfect square is not a primitive root modulo $p$ for any prime $p>3$

Trying to prove that if $n^2=3q$, then $n=3p$ for $n,p,q \in\mathbb{N}$.

How do I show that $n$ is prime if and only if $\phi(n) = n − 1$?

Which polynomials are "transitive" with respect to $\mathbb{Z}/r\mathbb{Z}$?

Show that if $x$ is a primitive root modulo $p^r$, then $x$ is a primitive root modulo $p$

Are there infinitely many numbers such that $ \phi(n)=\phi(n-1)+\phi(n-2)$?

"Find which coin is fake and which is genuine?"-A coin riddle on parity of numbers

Solution of the Diophantine Equation $x^2-ay+c=0.$

Prove that for every prime number $|\{1\leq x \leq p^2 : p^2 | (x^{p-1}-1) \}|=p-1$

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