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Prove that every composite number in Z is reducable
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.
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
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