Q.1 Show that the cube of any positive integer is of the form 4m,4m+1 or 4m+3 for some integer m?

Q.2 A number when divided by 609 gives remainder 65.What remainder would be obtained by dividing the same number by 29 ? (Hint:-Use Euclid's division algorithm).

Asked by DEVANSH MORE | 24th Apr, 2014, 12:10: PM

Expert Answer:

Q1: you can show this for three consecutive numbers like 2 , 3 and 4 . You will notice a pattern on the basis of that you can prove it.
2 cubed equals 8 equals 4 m  3 cubed equals 27 equals 4 n plus 3  4 cubed equals 4 p
Q2. l e t space n u m b e r space b e space N comma space t h e n  N equals 609 m plus 65  N o w space space i t space i s space d i v i d e d space b y space 29 comma space w e space g e t  N equals 21 n plus 7  T h u s comma space t h e space r e m a i n d e r space i s space 7.

Answered by  | 29th Apr, 2014, 09:08: AM

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