Q1.Find the largest number which divides 245 and 1029 leaving remainder 5 in each case. Q2. Prove that if x and y are odd positive integer, x>y then x 2 - y 2 is divisible by 4. Q3. Prove that exactly one out of every three consecutive integers is divisible by 3.

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Answers

2016-05-07T18:49:12+05:30
1.  245-5 = 240
1029-5 = 1024
hcf of 240 and 1024 = 16
therefore 245/16 = 15 (with remainder as 5)
1029/16 = 64 (with 5 as remainder)

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