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Prime Factorization and Divisors
Learn how to break down numbers big and small, as proposed by the Fundamental Theorem of Arithmetic.
Find the number of odd divisors of \(7!\)
by
Paul Ryan Longhas
Find smallest positive \(a\) for \(a={ b }^{ 2 }={ c }^{ 3 }={ d }^{ 5 }\) such that \(a,b,c,d\) are distinct integers.
by
shivamani patil
\[\large 6128704063125000=2^3\times 3^5 \times 5^7 \times 7^9\]
For the number above, find the number of divisors which are perfect squares.
by
Rushi Jogdand
For two non-negative integers \(a\) and \(b\) , the equation \({ 3\cdot 2 }^{ a }+1={ b }^{ 2 }\) has solutions \(({ a }_{ 1 },{ b }_{ 1 }),({ a }_{ 2 },{ b }_{ 2 }),...,({ a }_{ n },{ b }_{ n })\).
Find \({ a }_{ 1 }{ +b }_{ 1 }+{ a }_{ 2 }+{ b }_{ 2 }+...+{ a }_{ n }+{ b }_{ n }\)?
by
Isaac Jiménez
Given that \(x^{2} + 5x + 6\) is a prime number, determine the smallest integer value of \(x\).
Details and Assumptions:
- If you think no such solution exists, input \(999\) as your answer.
by
Theodore Jonathan