Determine-the-general-solution-of-the-following-linear-diophantine-equation-for-N-Z-m-Z-8N-81m-65-

Question Number 1156 by 112358 last updated on 06/Jul/15

D e t e r m i n e t h e g e n e r a l s o l u t i o n

o f t h e f o l l o w i n g l i n e a r d i o p h a n t i n e

e q u a t i o n f o r \forall N \in Z^{+}, m \in Z^{+} :

8 N = 81 m + 65 .

Commented by prakash jain last updated on 06/Jul/15

N \equiv 1 \times m + 1 (\mod 8)

m \equiv 7 (\mod 8)

Answered by prakash jain last updated on 06/Jul/15

m = 8 k - 1, k \in N

8 N = 81 \times (8 k - 1) + 65

8 N = 81 \times 8 k - 16

N = 81 k - 2