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Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

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Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

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This is a beautiful result involving a parabola and parallels.

Powerful Factors

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Factorise $5^{36}-1$ into as many factors as you can, until you can calculate the values and see which ones are even and which are multiples of $3$.