10 Answered Questions for the topic Elementary Number Theory

Are all highly composite numbers even?

A highly composite number is a positive integer with more divisors than any smaller positive integer. Are all highly composite numbers even (excluding 1 of course)? I can't find anything about this... more

How to multiply decimal with wholenumber?

Explain why gcd(a, b) = 1.

If 1 = sa + tb, where a, b, st ∈ Z, explain why gcd(a, b) = 1.    

Show [n(n^2−1)]/3 is an integer

Use the division algorithm to show [n(n^2−1)]/3 is an integer, for all n ∈ Z.

What is wrong with the claim that an 8x8 square can be broken into pieces that can be reassembled to form a 5x13 rectangle?

it says   "hint: where is the extra square unit"   am i supposed to use a proof here? if so is this Fibonacci, generalized Fibonacci, Lucas number?

Proof for Fibonacci numbers

Prove that   fn+1fn-1-fn2=(-1)n   for every positive integer n...

g is defined recursively by g(1)=2 and g(n)=2g(n-1) where n is greater than/equal to 2...solve for g(4)

that is g(n)=2g(n-1)   i think i am stuck on where to plug in what.... i know that a series/sequence defined recursively is g(n)=g(n+1)=(n+1)g(n) so if g(1)=2 then for the g(n)=2g(n-1)  for... more

find the values of the following products...... (SUPER PI ;)

i know that the general form for super pi is ∏ak=am*am+1,...,an  where k=m to n im cool with this if the limit is finite. but i get confused when my upper limit is n...   my specific problem... more

show that [x+y] is greater than or equal to [x]+[y] for all real numbers x and y

not sure what to do with these... the problem in my book reads show that [x+y] ≥ [x]+[y] for all reals x and y.....(brackets, not abs. value bars)

what is the value of [x]+[-x] where x is a real number?

is this as simple as just plugging in real numbers for x? if so, let's say x=1 then we have [1]+[-1] would be 0 so the value for all real numbers in this particular summation would always be... more

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