A343115 Numbers k such that k^2 divides 5^k - 3^k - 2^k.

1, 2, 3, 4, 5, 6, 8, 12, 15, 19, 24, 95, 361, 876

Offset: 1

Author

Thomas Ordowski, Apr 05 2021

Keywords

• nonn
• more

Comments

Are there only finitely many such numbers?

Primes in the sequence are A130076.

Next term, if it exists, exceeds 5*10^8. - Jon E. Schoenfield, May 07 2021

Crossrefs

Cf. A130072, A130073, A130076.

Programs

Maple

q:= k-> is(0=5&^k-3&^k-2&^k mod k^2):
select(q, [$1..1000])[];  # Alois P. Heinz, May 07 2021

Mathematica

Select[Range[1000], Mod[PowerMod[2, #, #^2] + PowerMod[3, #, #^2],#^2] == PowerMod[5, #, #^2] &] (* Amiram Eldar, Apr 05 2021 *)