4

Part of 2005 Austrian-Polish Competition

Problems(1)

FLT fraction is a square

Source: Austrian-Polish 2005, Problem 4

Determine the smallest natural number

a\geq 2

for which there exists a prime number

p

and a natural number

b\geq 2

\frac{a^p - a}{p}=b^2.

fermat's little theoremPerfect Squaresprimenumber theoryDiophantine equation