Hi, I am having a little trouble with this problem. Please see the attached document for more details. Thanks in advance for your assistance.
I need help with the following problem: Show that 3 is a quadratic nonresidue of all Mersenne primes greater than 3. Please show all work so that I understand the logic of each step of the proof. Thanks for the help.
I need help with this problem: (a) If p is an odd prime and q is an odd prime where q = 10p + 3, show that (p/q)=(3/p). (b) If p is an odd prime and q is an odd prime where q = 10p + 1, show that (p/q)=(-1/p). Please show all work so that I understand each step. Thanks for the help.
How many Pythagorean triangles (primitive or not) can you find with hypotenuse 1105? Please show all work. Thanks in advance for the help.
I pulled this question from the Pythagorean triangle chapter in my number theory book. Please help me to solve this problem. Here it is: If (a,b)=d and a^2 + b^2 = c^2, show that (a,c)=(b,c)=d. Please show as much detail as possible. Thanks in advance for the help.
I pulled this question from the Pythagorean triangle chapter in my number theory book. Please help me solve this problem. Here it is: If (a,b)=1 and ab=c^n, show that a and b are nth powers. Please show as much detail as possible. Thanks in advance for the help.
I pulled this question from the Pythagorean triangle chapter in my number theory book. Please help me to solve this problem. Here it is: If (a,b)=d and ab=c^n, show that a/d and b/d are not necessarily nth powers. Please explain each step. Thanks in advance for the help.
Here it is: a) Find two pythagorean triangles with the same area. b)Prove that two Pythagorean triangles with the same area and equal hypotenuses are congruent. Please show as much detail as possible. Thanks so much for the help.
Please help me with the following problem: a) 3^2 + 4^2 = 5^2 20^2 + 21^2 = 29^2 119^2 + 120^2 = 169^2 To find another such relation, show that if a^2 + (a+1)^2 = c^2, then (3a+2c+1)^2 + (3a+2c+2)^2 = (4a+3c+2)^2. (b) If a^2 + (a+1)^2 = c^2, let u=c-a-1 and v=(2a+1-c)/2. Show that v is an integer and tha ...continues
Fermat's and Wilson's Theorems
What is the remainder when 314^162 is divided by 7?
