Saved Bookmarks
| 1. |
Show that every even positive integer is of the form 5q+1 or 5q+3 for some integer q |
| Answer» Let p be any positive integer.On dividing p by 5 , Let M be Quotient and R be Remainder.Then , By Euclid division lemma , we havep = 5q+1 , where r = 0,1,2,3,4p = 5q , where R = 0p =5q + 1 , where R = 1p = 5q + 2 , where R = 2p = 5q + 3 , where R = 3p = 5q + 4 , where R = 4p = 5q , 5q+2 , 5q+4 are even values of N.ThusWhen p is odd , it is in the form of 5q , 5q+1 and 5q+3.\xa0 | |