Grade 8 Math
posted by Sara .
URGENT HELP!Squares into Primes
Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2.
Find all the primes less than 100 that can be each written in all three ways: p=a^2+b^2=c^2+2 e^2= f^2+3 g^2, and show how its done with each one (as above with 13, 11, and 31) The numbers you are squaring must be integers; show your thinking!