porve that if st are integers then s24t not equal to 2Soluti

porve that:

if s,t are integers, then s^2-4t not equal to 2

Solution

Well,

let\'s suppose we have s and t so that :
s^2 - 4t = 2
then :
s^2 = 4t + 2 = 2(2t+1)

which is impossible, because : if 2 is present is the divisors of s^2,
then it is present in the divisors of s
AND : if 2 is present in the divisors of s then, we not only have 2^1 present among the divisors of s^2 but at least 2^2
and this is in contradiction with : s^2 = 2(2t+1) : 2 times an ODD number, which means that 2 is only present at the power 1.

therefore : for all integers s,t:
s^2 - 4t != 2