Page 60 - Numbertheory

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564 × 825 = 564 × 275 = 1064 × 211
1064

. 211 = 2048
. 2 + 0 + 4 + 8 = 14

9 AB9 [Mathcounts 2010] ( )

86 ( ) 7 34 ( ) BA7

62 ( ) 31 ( )

: ()

AB9 = (A × 9 + B )10
BA7 = (B × 7 + A )10

.A = 3B . 9A + B = 7B + A
.A =3
4

B =4

349 = 3× 9 + 4 = 31

437 = 4 × 7 + 3 = 31

. 31

.12b ×15b ×16b = (3146)b [AHSME 1967] ( )

sb . sb = 12b + 15b +16b

44 ( ) 42 ( ) 40 ( ) 38 ( )

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