1. prove that any +ve integer of the form 3a+2,for some integer a;[but not conversely]

Asked by aninadathoorsridharan | 7th May, 2016, 06:47: PM

Expert Answer:

L e t space c space b e space a n y space p o s i t i v e space i n t e g e r space a n d space d equals 3. N o w space a p p l y i n g space E u c l i d apostrophe s space D i v i s i o n space L e m m a space t h e r e space e x i s t space i n t e g e r s space apostrophe a apostrophe space a n d space apostrophe r apostrophe space s u c h space t h a t comma c equals 3 a plus r comma space w h e r e comma space 0 less or equal than r less than 3 T h u s comma space 0 less or equal than r less than 3 rightwards double arrow r equals 0 space o r space r equals 1 space o r space r equals 2 T h u s comma space w e space h a v e comma c equals 3 a space o r space c equals 3 a plus 1 space o r space c equals 3 a plus 2 comma space w h e r e space a space i s space s o m e space i n t e g e r T h e r e f o r e comma space a n y space p o s i t i v e space i n t e g e r space i s space o f space t h e space f o r m space 3 a plus 2 P l e a s e space c h e c k space t h e space q u e s t i o n. S o m e space d a t a space i s space m i s sin g.

Answered by Vimala | 8th May, 2016, 06:13: PM

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