MathLabs

Problem 2

For a positive integer kk, call an integer a pure kk-th power if it is mkm^k for some integer mm. Show that for every positive integer nn there exist nn distinct positive integers whose sum is a pure 20092009-th power and whose product is a pure 20102010-th power.
Step 4 of 7: Choose the scaling exponent
Previous stepNext step
x=k2−1x=k^2-1
Detailed analysis

Use x=k2−1x=k^2-1. Then x≡−1(modk)x\equiv-1\pmod k and x≡0(modk+1)x\equiv0\pmod{k+1}.