10 Answered Questions for the topic Elementary Number Theory

Elementary Number Theory Prealgebra Prime Numbers Prime Factorization


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
Elementary Number Theory Gre Elementary Math Decimal Expansion


How to multiply decimal with wholenumber?

Elementary Number Theory Integers Greatest Common Factor Number Theory


Explain why gcd(a, b) = 1.

If 1 = sa + tb, where a, b, st ∈ Z, explain why gcd(a, b) = 1.    
Elementary Number Theory Integers Number Theory Division Algorithm


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.
Elementary Number Theory


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?
Elementary Number Theory


Proof for Fibonacci numbers

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


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
Elementary Number Theory


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
Elementary Number Theory


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)
Elementary Number Theory


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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