Fermat's and Wilson's Theorems

Please help me with this problem: What is the remainder when 314^164 is divided by 165? (Watch out - 165 is not prime!) Please show all work. Thanks in advance for the help.

Fermat's and Wilson's Theorems

Please help me with this problem: What is the remainder when 2001^2001 is divided by 26? Please show all work. Thanks in advance for the help.

Pythagorean Triangles

Please help me with the following problem: a) Prove that two Pythagorean Triangles with the same area and equal hypotenuses are congruent. b) Find two Pythagorean triangls with the same area. Please show all work. Thanks in advance for the assistance.

Calculate the number of subsets and the number of proper subsets for the set

{xlx is a u.s. coin worth less than a dollar} Between the x's is a line. Used l closest thing

The set of subsets of {a,e,i,o,u} contains 64 elements. Please explain.

The set of subsets of {a,e,i,o,u} contains 64 elements. Please explain.

Calculate the number of subsets and the number of proper subsets for each set

{a,b,c,d,e,f}

Wilson's thm

Prove that if p is a prime, then (p - 2)! is congruent to 1 (mod p)

Chinese remainder theorem

Solve the egg problem used to illustrate the Chinese Remainder Theorem if the remainders on division by 2,3,4,5,6 and 7 are all 1 by (i) the given procedure (ii) the "easier" way