Prove that there are no integer solutions to the equation x² = 4y + 3. Prove that every prime number greater than 3 is either one more or one less than a multiple of 6.

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Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

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Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

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Q: If a, b, c are positive real numbers. Then prove that (a + 1)(b + 1) (c + 1)² >77 abct.

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