1975 AHSME Problems/Problem 22
Revision as of 22:37, 6 January 2020 by Brainiacmaniac31 (talk | contribs) (Created page with "Since the roots are both positive integers, we can say that <math>x^2-px+q=(x-1)(x-q)</math> since <math>q</math> only has <math>2</math> divisors. Thus, the roots are <math>1...")
Since the roots are both positive integers, we can say that 
since 
only has 
divisors. Thus, the roots are 
and and 
. The only two primes which differ by are 
so 
and 
.
is true because 
.
is true because one of the roots is which is prime.
is true because 
is prime.
is true because 
is prime.
Thus, the answer is 
.
