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Some diagrammatic 'proofs' of algebraic identities and inequalities.
By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn
By proving these particular identities, prove the existence of general cases.
Use the fact that: x²-y² = (x-y)(x+y) and x³+y³ = (x+y) (x²-xy+y²) to find the highest power of 2 and the highest power of 3 which divide 5^{36}-1.