10

Part of 2007 Pre-Preparation Course Examination

Problems(1)

A subset- Iran 3rd round-Number Theory 2007

Source:

a >1

be a positive integer. Prove that the set

\{a^2+a-1,a^3+a-1,\cdots\}

S

with infinite members and for any two members of

S

x,y

\gcd(x,y)=1

. Then prove that the set of primes has infinite members.

number theory unsolvednumber theory