Preparation for math olympiad UKMT junior senior intermediate maths challenge smc jmc imc 2022 2023

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[jim]

Too confusing and too tedious. We know the bases have to be small because 13 is relatively small and so is 35. By inspection 3^2 + 2^2 = 9 + 4 = 13. And 3^3 + 2^3 = 27 + 8 = 35. So x + y = 3 + 2 = 5.

[kfjfkeofitorhf]

X+y=11
X^2+y^2=13
X^3+y^3=35
X+Y=11