Page 53 - Numbertheory
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abcabc [AHSME 1951] ( )
101 ( ) 1001 ( ) 13 11 ( ) 11 7 ( )
:( )
abcabc = abc ×103 + abc
= abc (103 +1)
= abc ×1001
1417 1059 [AHSME 1976] ( )
d −r r d 2312
23 ( ) 19 ( ) 17 ( ) 15 ( )
2312 1417 1059 : ()
q3 q2 q1 d
1059 = q1d + r
1417 = q2d + r
2312 = q3d + r
1417 −1059 = 358 = (q2 −q1)d
2312 −1417 = 895 = (q3 − q2)d
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