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: d) How many non-negative integer solutions are there to the following problem? I1 + x2 + I3 = 10…

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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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: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

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Q: Show that V3 +2/6 is an irrational number.

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Q: Show that the cubed root of 2 is irrational by contradiction

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