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Combinatorics | Number Theory
1. How many of first 100 terms in the sequence 3, 5, 7, 9, 11, 13, 15...... are
divisible by 6?
2. 26th March is the Independence Day of Bangladesh. Independence of
Bangladesh was declared on 26/03/1971. Find out the largest number that can be
formed by taking multiplication of any two out of all the prime factors of the
product of 26, 03 and 2010.
divisible by 6?
2. 26th March is the Independence Day of Bangladesh. Independence of
Bangladesh was declared on 26/03/1971. Find out the largest number that can be
formed by taking multiplication of any two out of all the prime factors of the
product of 26, 03 and 2010.
Combinatorics | Number Theory
1. Let S= 1^1 + 2^2+3^3+.....+2010^2010. . What is the remainder when S is divided by 2?
2. Find the number of odd coefficients in expansion of (x + y)^2010.
3. Find all prime numbers p and integers a and b (not necessarily positive) such that p^a + p^b
is the square of a rational number.
2. Find the number of odd coefficients in expansion of (x + y)^2010.
3. Find all prime numbers p and integers a and b (not necessarily positive) such that p^a + p^b
is the square of a rational number.
Combinatorics | Number Theory
Prove that every composite number in Z is reducable
Combinatorics | Number Theory
Find the number of terms free from the radical sign in {(7)^(1/3) + (11)^(1/9)}^(654) .
Combinatorics | Number Theory
(x^1+x^2+............+x^100)^500 if you apply binomial theorem how many digits there will be
Combinatorics | Number Theory
If P_n=6^n+8^n,
(P_83÷49) what is the remainder?
(P_83÷49) what is the remainder?
Combinatorics | Number Theory
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.
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.
Combinatorics | Number Theory
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.
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.
Combinatorics | Number Theory
GCF of 22 and 99
Combinatorics | Number Theory
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?
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#340153 on Dec 2023
#340153 on Dec 2023