Question: The congruence equation ′′ ( 5a +3 )x ≡^(3a + 4) 19 ′′ is given. Find the sum of digits of the smallest three −digit natural number ” a ” such that the assumed equation has no solution in ” Z ”.


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Question Number 201897 by mnjuly1970 last updated on 15/Dec/23

$Q u e s t i o n : T h e c o n g r u e n c e$ $e q u a t i o n^{″} (5 a + 3) x \overset{3 a + 4}{\equiv} 19^{″} i s g i v e n .$ $F i n d t h e s u m o f d i g i t s o f$ $t h e s m a l l e s t t h r e e - d i g i t n a t u r a l n u m b e r^{″} a^{″}$ $s u c h t h a t t h e a s s u m e d e q u a t i o n h a s$ $n o s o l u t i o n i n^{″} Z^{″} .$
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