Waste less time on Facebook — follow Brilliant.
Already have an account? Log in here.
Prime Factorization and Divisors
Learn how to break down numbers big and small, as proposed by the Fundamental Theorem of Arithmetic. See more
Find the number of odd divisors of \(7!\)
Already have an account? Log in here.
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.
Already have an account? Log in here.
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.
Already have an account? Log in here.
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 \({ a }_{ 1 }{ +b }_{ 1 }+{ a }_{ 2 }+{ b }_{ 2 }+...+{ a }_{ n }+{ b }_{ n }\)?
Already have an account? Log in here.
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.
Already have an account? Log in here.
by
Theodore Jonathan