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Challenge 3 The following result was found by Euler, but Ilve changed his numbers to A and B to
make your life hard. Theorem: A prime number p can be expressed in the form x2+3y2 If and only
if p is congruent to A modulo B (i.e., DB=A ). Use experimental techniques to determine A and B.
Now try the same for 3 replaced by 4,5,6,7,8,9.

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Challenge 3 The following result was found by Euler but Ilv.pdf

  • 1. Challenge 3 The following result was found by Euler, but Ilve changed his numbers to A and B to make your life hard. Theorem: A prime number p can be expressed in the form x2+3y2 If and only if p is congruent to A modulo B (i.e., DB=A ). Use experimental techniques to determine A and B. Now try the same for 3 replaced by 4,5,6,7,8,9.