Question

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Answer 1

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Answer 2

Answer:

7. let us start with taking a ,where a is a positive odd integer.we apply the division algorithm with a and b=4. since 0<r<4 the possible remainders are 0,1,2,and 3.that is a can be 4q,or 4q+1,or 4q+3, where a is the quotient . however, since a is odd, a cannot be 4q or 4q+2(since they are both divisible by 2). therefore, any odd integer is the form 4q+1 or 4q+3.