Show that phi(n) = n/2 if and only if n = 2k for some positive integer k. Please see attached for the details of the problem.
I need help with this problem. Here it is: Bhascara found a right triangle whose area is numerically equal to the length of its hypotenuse. Show that this cannot happen if the triangle has integer sides. Please be detailed as possible. I appreciate your help.
Hi, I need help with this problem, don't quite know how to solve it. Please see that attached document for more details. Thanks in advance for your help.
I need assistance working out this problem. Please see the attached document for more details. Thanks in advance for your assistance.
Please see the attached file for the fully formatted problems. Theorem: If p is an odd prime, then (2/p) = 1 if p 1 or 7 (mod 8) (2/p) = -1 if p 3 or 5 (mod 8) Show that the theorem stated above can be rewritten as for odd primes p.
Please see the attached file for the fully formatted problems. The Quadratic Reciprocity Theorem – If p and q are odd primes and , then (p/q) = -(q/p). Otherwise , (p/q) = (q/p). Show that the quadratic reciprocity theorem could be rewritten as for odd primes p and q.
Please see the attached file for the fully formatted problems. Prove that if p 3 (mod 8) and (p–1)/2 is prime, then (p–1)/2 is a quadratic residue (mod p).
Please see the attached file for the fully formatted problems. (a) Prove that if p 7 (mod 8), then p | . (b) Find a factor of . Note: Please show as much detail as possible (so that I understand the problem and the logic behind each step). Thanks!
Please see the attached file for the fully formatted problems. (a) Show that if p 3 (mod 4) and a is quadratic residue (mod p), then p – a is a quadratic nonresidue (mod p). (b) What if p 1 (mod 4)?
Hi, I am having a little trouble with this problem. Please see the attached document for more details. Thanks in advance for your assistance.
