Combinatorics | Number Theory Answers

prove that gcd (n-1, n+1)= 1 or 2 for each n>=2 and gcd (2n-1, 2n+1)= 1 for each n>=7.

Let a, b, c be any three integers. Define gcd(a, b, c), the gcd od a, b, c as a positive integer d such that
(i) d|a, d|b, d|c and
(ii) if f|a, f|b, f|c then f|c
prove that gcd(a, b, c) =gcd(a, (b,c)) =gcd ((a,b),c) = gcd ((a,c),b)

When eggs in a basket are taken out 2, 3 , 4, 5 , 6at a time, there remain respectively 1, 2, 3, 4, 5 eggs; while the number comes even when they are taken out seven at a time. Find the smallest number of eggs in basket.

solve the linear congruence 17x≅9(mod 276), by using Chinese Remainder Theorem.

If a pizza costs £2.85 to produce and is sold to the guest for £9.95, what percentage gross profit is made from this dish?

Explain how would you find the empirical probability of rolling a 4 on a die?

A card is drawn at random from a standard deck. Find the theoretical probability that the card is neither an ace nor a heart.

A card is drawn at random from a well shuffled deck of 52 cards. What is the theoretical probability of drawing a face card or a spade?

find the product of the following decimal numbers by drawing horizontal vertical lines and shading