4

Part of 1981 Bundeswettbewerb Mathematik

Problems(1)

2^p + 3^p=a^n Italian TST problem

Source: Italy TST 1999

Prove that for any prime number

p

2^p+3^p=a^n

has no solution

(a,n)

in integers greater than

1

modular arithmeticnumber theory proposednumber theory