Determine whether the equation $$x^4+y^3=z!+7$$has an infinite number of solutions in positive integers.
Problem
Source: Baltic Way 2017
Tags: number theory, factorial, equation
rkm0959
11.11.2017 17:17
$\pmod{13}$ says hi
Vrangr
11.11.2017 17:19
rkm0959 wrote: $\pmod{13}$ says hi Inspiration behind using $\pmod{13}$?
rkm0959
11.11.2017 17:44
$4 \cdot 3 +1 = 13$
timon92
11.11.2017 19:10
This problem was proposed by me
FedeX333X
11.11.2017 20:06
rkm0959 wrote: $\pmod{13}$ says hi Ouch you completely spoiled me the problem
AlirezaOpmc
11.11.2017 20:20
rkm0959 wrote: $4 \cdot 3 +1 = 13$ It's because of Euler.
AwesomeYRY
10.10.2021 18:15
No. For $z\geq 13$ in mod 13 we have \[\{3,9,1\} + \{ 8, -1, -8, 1\} = 0 + 7\]