MathDB

Problem 12

Part of 2019 LIMIT Category A

Problems(2)

a!b!c!d!=24!

Source: LIMIT 2019 CAS1 P12

4/28/2021
Compute the number of ordered quadruples of positive integers (a,b,c,d)(a,b,c,d) such that a!b!c!d!=24!a!b!c!d!=24!<spanclass=′latex−bold′>(A)</span> 4<span class='latex-bold'>(A)</span>~4 <spanclass=′latex−bold′>(B)</span> 4!<span class='latex-bold'>(B)</span>~4! <spanclass=′latex−bold′>(C)</span> 44<span class='latex-bold'>(C)</span>~4^4 <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
combinatoricsDiophantine equationnumber theory
taxicab number

Source: LIMIT 2019 CAS2 P12

4/28/2021
What is the smallest positive integer nn such that n=x3+y3n=x^3+y^3 for two different positive integer tuples (x,y)(x,y)?
number theory