10 Answered Questions for the topic Elementary Number Theory

03/19/19

#### 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...
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10/08/17

#### 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.

09/11/14

#### 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?

09/08/14

#### 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...
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09/08/14

#### 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...
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09/05/14

#### 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)

09/05/14

#### 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...
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