1

Part of 2013 Czech-Polish-Slovak Junior Match

Problems(2)

\sqrt{x-\sqrt{y}}+ \sqrt{x+\sqrt{y}}= \sqrt{xy} diophantine

Source: Czech-Polish-Slovak Junior Match 2013, Individual p1 CPSJ

Determine all pairs

(x, y)

of integers for which satisfy the equality

\sqrt{x-\sqrt{y}}+ \sqrt{x+\sqrt{y}}= \sqrt{xy}

Diophantine equationdiophantinenumber theoryradical

infinite primes p having a multiple in the form n^2 + n + 1 ?

Source: Czech-Polish-Slovak Junior Match 2013, Team p1 CPSJ

Decide whether there are infinitely many primes

p

having a multiple in the form

n^2 + n + 1

for some natural number

n

primesnumber theoryinfinitely many