Question

Solution : 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<<4, the possible remainders are 0, 1, 2 and 3.
That is, a can be 4q, or 4q+1, or 4g + 2, or 4q+3, where q is the quotient. However,
since a is odd, a cannot be 49 or 49+2 (since they are both divisible by 2).
Therefore, any odd integer is of the form 4q+1 or 49 + 3.
EXERCISE - 1.1
1.
Use Euclid's division algorithm to find the HCF of
(i) 900 and 270 (ii) 196 and 38220 (iii) 1651 and 2032
foan
Use Euclid division lemma to show that any positive odd integer is of the form 6q+1, or
69 + 3 or 6q+5, where q is some integers.
Use Euclid's division lemma to show that the square of any positive integer is of the form
3p, 3p +1.
Use Euclid's division lemma to show that the cube of any positive integer is of the form
9 m, 9m + 1 or 9m + 8.​

Answer 1

Answer:

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