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Challenge 420: Sums of powers

When are these sums of powers squares or cubes?

a) How many values of n can you find so that 26 + 210 + 2n is a square number?

b) How many values of n can you find so that 33 + 36 + 39 + 3n is a cube number?

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.