3

Problems(1)

Diophantine equation with prime number and power of 3

Source: 2015 Turkey Junior National Olympiad P3

12/7/2015

Find all pairs

(p,n)

so that

p

is a prime number,

n

is a positive integer and

p^3-2p^2+p+1=3^n

holds.

number theoryDiophantine equationprime numbers