divisibility of sum of integers raised to odd powers

Prove that for all odd integers n, (1^n)+(2^n)+(3^n)…+(n^n) is a proper multiple of 1+2+3+…n

number theory

write the numbers 25, 32, 56 to the base 5. write 47, 68, 127 to the base 2.

euclid's division lemma / fundamental theorem of arithmetic

please see attached problems 2 credits/problem theorem 2-1 is euclid's division lemma j=qk+r

divisibility

find the greatest common divisor of the following pairs: a)527, 765 (use technique like 527=341*1+186) b)361, 1178 (use technique like 527=341*1+186) c) -find the gcd (d) of 299, 481 (use technique like 31=186-155*1 --> 31=186-(341-186*1) -find integers such that 299x+481y=d -now replace 299 and 481 by 129 and 301

Fundamental Theorem of Arithemtic

Please solve the following problems: 1. Compute the following ... 2. Let Fm be the set of all integral multiples of the integer m. Prove that ... 3. Draw the graphs of the straight lines defined by the following Diophantine equations ... 4. Prove that every integer is uniquely representable as the product of a non-negative power of 2 ... and an odd number ... *(Please see attachment for complete problems)