Advertisements
Advertisements
प्रश्न
Prove that the square of any positive integer of the form 5q + 1 is of the same form.
उत्तर
Let n = 5q + 1 where q is a positive integer
∴ n2 = (5q + 1)2
= 25q2 + 10q + 1
= 5(5q2 + 2q) + 1
= 5m + 1, where m is some integer
Hence, the square of any positive integer of the form 5q + 1 is of the same form.
APPEARS IN
संबंधित प्रश्न
Show that any positive integer which is of the form 6q + 1 or 6q + 3 or 6q + 5 is odd, where q is some integer.
Find the simplest form of `1095 / 1168` .
Find the maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils.
What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?
Determine the number nearest to 110000 but greater than 100000 which is exactly divisible by each of 8, 15 and 21.
The least number that is divisible by all the numbers from 1 to 8 (both inclusive) is ______.
Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.
Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
Show that the square of any odd integer is of the form 4q + 1, for some integer q.
