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How many prime numbers p are there such that 29 raised to the power p plus 1 is a multiple of p?
To solve this problem, we can use Fermat's Little Theorem, which states that if p is a Prime number and a is any integer, then a^p ≡ a (mod p). Given that 29^p + 1 is a multiple of p, we can rewrite this as 29^p ≡ -1 (mod p). This implies that p must be a prime of the form 4k + 1, where k is a non-negative integer. Therefore, there are infinitely many prime numbers p that satisfy the given condition.
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What is the prime factorization of 630 using exponents?
The prime factorization of 630 is 2 x 3^2 x 5 x 7. This means that 630 can be expressed as the product of these prime numbers raised to their respective exponents. In this case, we have 2 raised to the power of 1, 3 raised to the power of 2, 5 raised to the power of 1, and 7 raised to the power of 1.
What is the prime factorization of 2x2x2x3x3x5?
As a product of its prime factors: 2*2*2*3*3*5 = 360
What is 80 in the product of its prime factors?
The prime factorization of 80 is 2^4 * 5. This means that 80 can be expressed as the product of the prime numbers 2 and 5 raised to certain powers. In this case, 2 is raised to the power of 4 and 5 is raised to the power of 1.
What is the least common multiple of two different prime numbers?
The least common multiple of two different prime numbers is the product of those two prime numbers.
What is the least common multiple of 2149?
There is no LCM for less than two numbers. LCM is the multiple of the highest power of prime factors in two or more numbers. Example: LCM of 9, 15, and 25 is 225, which is the multiple of the highest power of prime factors in 9, 15, and 25 (32 x 52).
Which numbers have a prime factorization that are all equal?
Any prime number raised to a power.
What is greatest prime number raised to the 3rd power?
There are infinitely many prime numbers and there is no greatest prime. So there cannot be an answer to the question.
What is the prime factorization of 630 using exponents?
The prime factorization of 630 is 2 x 3^2 x 5 x 7. This means that 630 can be expressed as the product of these prime numbers raised to their respective exponents. In this case, we have 2 raised to the power of 1, 3 raised to the power of 2, 5 raised to the power of 1, and 7 raised to the power of 1.
What is the multiple of 192 to the power of their prime numbers?
2^6 x 3 = 192
What is the prime factorization of 2x2x2x3x3x5?
As a product of its prime factors: 2*2*2*3*3*5 = 360
What is 80 in the product of its prime factors?
The prime factorization of 80 is 2^4 * 5. This means that 80 can be expressed as the product of the prime numbers 2 and 5 raised to certain powers. In this case, 2 is raised to the power of 4 and 5 is raised to the power of 1.
What is the least common multiple of two different prime numbers?
The least common multiple of two different prime numbers is the product of those two prime numbers.
Is there a product of two perfect squares that is not a perfect square?
No there isn't. every perfect square number can be factored into prime number. At their factoration you'll always have multiples of two on the primes exponent. Therefore you'll multiply a prime raised to a 2-multiple number with another prime raised to a 2-multiple number wich gives you also a number that factored gives you a product of prime numbers raised to a 2-multiple number and so, a perfect square.
How many prime numbers p are there such that 29 to the power p plus 1 is a multiple of p?
42
What is the least common multiple of 2149?
There is no LCM for less than two numbers. LCM is the multiple of the highest power of prime factors in two or more numbers. Example: LCM of 9, 15, and 25 is 225, which is the multiple of the highest power of prime factors in 9, 15, and 25 (32 x 52).
What is a prime number 48 multiple?
2 and 3 are prime numbers 48 is a multiple of.
What is the least common multiple of 34?
There is no LCM for less than two numbers. LCM is the multiple of the highest power of prime factors in two or more numbers. Example: LCM 0f 9, 15, and 25 is 225, which is the multiple of the highest power of prime factors in 9, 15, and 25 (32 x 52).
