is a fraction an integer

is a fraction an integer A handy way of calculating for real fractions with even denominators is 1 2 n 2n 4nn Where n is an integer But keep in mind that the gamma function is actually the factorial of 1 less than the number than it evaluates so if you want 3

An integer is any whole number or its negative e g 2 1 0 1 2 A non zero integer is any of these but 0 Your definition of a rational number is just a mathematically rigorous way of saying that a rational number is any fraction of whole numbers possibly with negatives and you can t have 0 in the denominator Share There are exactly four integer values of a for which 2a b a 2 is itself an integer This is only true for certain values of b only For how many values of b in the range 1 b 20 is the statement true My thought process so far I m trying to work out when there will only be four values which a and so far I cannot think of anything

is a fraction an integer

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is a fraction an integer
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begingroup Oddly enough I had never seen the very elementary claim that some integer clears any algebraic number into an algebraic integer and I had to think about it for a minute Plus 1 for making me realize something obvious endgroup So n 1 divides the denominator but not the numerator contra the fraction is an integer

See my post here for a simple purely arithmetical proof that every binomial coefficient is an integer The proof shows how to rewrite any binomial coefficient fraction as a product of fractions whose denominators are all coprime to any given prime rm p This implies that no primes divide the denominator when written in lowest terms therefore the 1 Simply write a c b a c b as an irreductible fraction and this will give you the lowest integer c c and b b Example a 0 2525 2525 10000 101 400 a 0 2525 2525 10000 101 400 yields b 400 b 400 and c 101 c 101 c c is minimal because b c b c are coprime integers But that s not what I m asking

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K 1 1 always divides n n k 1 1 Hint Use Induction on Pascal s Triangle to demonstrate that n k is always an integer Then demonstrate that the quotient equals n k n 1 k 1 Edit I mistakenly thought that the RHS LHS simplified to n k n 1 k 1 This is wrong Consider the question frac 12 2 in mathbb Z Would you consider the above statement mathematically correct and why

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is a fraction an integer - 1 Simply write a c b a c b as an irreductible fraction and this will give you the lowest integer c c and b b Example a 0 2525 2525 10000 101 400 a 0 2525 2525 10000 101 400 yields b 400 b 400 and c 101 c 101 c c is minimal because b c b c are coprime integers But that s not what I m asking