Combinatorics | Number Theory Answers

Find the number of terms free from the radical sign in {(7)^(1/3) + (11)^(1/9)}^(654) .

(x^1+x^2+............+x^100)^500 if you apply binomial theorem how many digits there will be

If P_n=6^n+8^n,
(P_83÷49) what is the remainder?

1. Theorem Let a,b and c be integers with a and b not both 0. If x = x0, y = y0 is an integer solution to the equation ax + by = c (that is, ax0 + by0 = c, then for every integer k, the numbers x = x0 + kb0 (a,b) and y = y0 − ka (a,b)
are integers that also satisfy the linear Diophantine equation ax + by = c. Moreover, every solution to the linear Diophantine equation ax + by = c is of this form.

2. Exercise Find all integer solutions to the equation 24x + 9y = 33.

3. Theorem Let a and b be integers with a,b > 0. Then gcd(a,b)· lcm(a,b) = ab.

1. Theorem Let a,b and c be integers with a and b not both 0. If x = x0, y = y0 is an integer solution to the equation ax + by = c (that is, ax0 + by0 = c, then for every integer k, the numbers x = x0 + kb0 (a,b) and y = y0 − ka (a,b)
are integers that also satisfy the linear Diophantine equation ax + by = c. Moreover, every solution to the linear Diophantine equation ax + by = c is of this form.

2. Exercise Find all integer solutions to the equation 24x + 9y = 33.

3. Theorem Let a and b be integers with a,b > 0. Then gcd(a,b)· lcm(a,b) = ab.

1. Theorem Let a,b and c be integers with a and b not both 0. If x = x0, y = y0 is an integer solution to the equation ax + by = c (that is, ax0 + by0 = c, then for every integer k, the numbers x = x0 + kb0 (a,b) and y = y0 − ka (a,b)
are integers that also satisfy the linear Diophantine equation ax + by = c. Moreover, every solution to the linear Diophantine equation ax + by = c is of this form.

2. Exercise Find all integer solutions to the equation 24x + 9y = 33.

3. Theorem Let a and b be integers with a,b > 0. Then gcd(a,b)· lcm(a,b) = ab.

These are three diffrent equations that i need help with please.

GCF of 22 and 99

Sayem is counting the minimum number of lines m, that can be drawn on the plane so that they interact in exactly 200 distinct points. What is m?

How many numbers between 8 and 840 have a remainder of 3 when divided by 7

A cricket team of 11 players is to be selected from two groups of 6 and 8 players. In how many ways can the selection be made so that at least 4 players are taken from the group of 6.