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Question Number 125959 by bramlexs22 last updated on 15/Dec/20

	Answered by liberty last updated on 15/Dec/20

	$L e t q d e n o t e t h e n u m b e r s o f e g g s o r i g i n a l l y$ $i n t h e b a s k e t . W e w a n t t o f i n d t h e l e a s t n u m b e r$ $o f e g g s i n t h e b a s k e t .$ $\Leftrightarrow q \equiv 1 (m o d 2) \equiv 1 (m o d 3) \equiv 1 (m o d 5) \equiv 0 (m o d 7)$ $t h e f i r s t t h r e e c o n g r u e n c e s t h e n$ $q \equiv 1 (m o d l c m (2, 3, 5)) = 30$ $s o l v i n g t h i s w i t h t h e r e m a i n i n g c o n g r u e n c e$ $g i v e s u s q \equiv 91 (m o d 210) . T h u s t h e$ $l e a s t n u m b e r o f e g g s i s 91 .$
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