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
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] would be 0 so the value for all real numbers in this particular summation would always be... more