Saturday

August 23, 2014

August 23, 2014

Posted by **Sara** on Monday, September 28, 2009 at 10:32pm.

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!

- Grade 8 Math -
**MathMate**, Tuesday, September 29, 2009 at 7:59amThis has been posted and answered recently. If you need more help, tell us where you have a problem.

See:

http://www.jiskha.com/display.cgi?id=1253825444

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