Using Euclid's Division Lemma, any positive integer is 5q, 5q+1, 5q+2, 5q+3 or 5q+4. For how many of these five forms is the square of the integer of the form 5m (a multiple of 5)?

Question

Accepted Answer

1. Squares: (5q)^2 = 5m; others give remainders 1,4,4,1 mod 5. Only 5q gives a square divisible by 5. So 1 form.

Using Euclid's Division Lemma, any positive integer is $5 q, 5 q + 1, 5 q + 2, 5 q + 3$ or $5 q + 4$ . For how many of these five forms is the square of the integer of the form 5m (a multiple of 5)?

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More Class 10 Euclid's Division Lemma practice

Using Euclid's Division Lemma, any positive integer is 5q,5q+1,5q+2,5q+3 or 5q+4. For how many of these five forms is the square of the integer of the form 5m (a multiple of 5)?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Euclid's Division Lemma practice

Using Euclid's Division Lemma, any positive integer is $5 q, 5 q + 1, 5 q + 2, 5 q + 3$ or $5 q + 4$ . For how many of these five forms is the square of the integer of the form 5m (a multiple of 5)?