Advertisements
Advertisements
प्रश्न
Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4
उत्तर
Let the integer be x
The square of its integer is x2
Let x be an even integer
x = 2q + 0
x2 = 4q2
When x is an odd integer
x = 2k + 1
x2 = (2k + 1)2
= 4k2 + 4k + 1
= 4k (k + 1) + 1
= 4q + 1 ......[q = k(k + 1)]
It is divisible by 4
Hence it is proved
APPEARS IN
संबंधित प्रश्न
Define HOE of two positive integers and find the HCF of the following pair of numbers:
100 and 190
Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.
Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.
Three pieces of timber 42m, 49m and 63m long have to be divided into planks of the same length. What is the greatest possible length of each plank? How many planks are formed?
Find the least number of square tiles required to pave the ceiling of a room 15m 17cm long and 9m 2cm broad.
Find the missing numbers in the following factorization:
The LCM and HCF of two numbers are 180 and 6 respectively. If one of the numbers is 30, find the other number.
The smallest rational number by which \[\frac{1}{3}\] should be multiplied so that its decimal expansion terminates after one place of decimal, is
Prove that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer.
Assertion: If the HCF of 510 and 92 is 2, then the LCM of 510 and 92 is 32460.
Reason: As HCF (a, b) × LCM (a, b) = a × b
