Project Euler

project euler 0135 - Same differences

project euler 0136 - Singleton difference

Hint:

$$x^2 - y^2 - z^2 = n$$ $$x = z + 2a$$ $$y = z + a$$ $$(z + 2a)^2 - (z + a)^2 - z^2 = n$$ $$(3a - z)(a + z) = n$$

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project euler 0139 - Pythagorean tiles

Hint:

• Primitive Pythagorean triples
• Suppose we have a^2 + b^2 = c^2, then abs(a - b) = 0 (mod c).

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project euler 0211 - Totient Chains

Hint:

• Sieve

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project euler 0214 - Totient Chains

Hint:

• Totient
• Sieve