Solve the 2nd question plzzzz!!!!
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Let be any positive integer
We know by Euclid's algorithm, if a and b are two positive integers, there exist unique integers q and r satisfying,where.
Take
Since 0 ≤ r < 4, the possible remainders are 0, 1, 2 and 3.
That is, can be , where q is the quotient.
Since is odd, cannot be 4q or 4q + 2 as they are both divisible by 2.
Therefore, any odd integer is of the form 4q + 1 or 4q + 3
We know by Euclid's algorithm, if a and b are two positive integers, there exist unique integers q and r satisfying,where.
Take
Since 0 ≤ r < 4, the possible remainders are 0, 1, 2 and 3.
That is, can be , where q is the quotient.
Since is odd, cannot be 4q or 4q + 2 as they are both divisible by 2.
Therefore, any odd integer is of the form 4q + 1 or 4q + 3
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