Competition problem — Algebra — Maths Olympiad Prep

Library / /84 of 168

Algebra Difficulty 1.8 Junior Find the answer

What is the value of $1^{3}+2^{3}+3^{3}+4^{3}$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Expanding and simplifying, $1^{3}+2^{3}+3^{3}+4^{3}=1 \times 1 \times 1+2 \times 2 \times 2+3 \times 3 \times 3+4 \times 4 \times 4=1+8+27+64=100$ . Since $100=10^{2}$ , then $1^{3}+2^{3}+3^{3}+4^{3}=10^{2}$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.