Question
When a number is divided by 114, remainder is 82. What
will be the remainder when the cube of the number is divided by 19?Solution
114)N( 
                                  82 
 remainder N = 114x+ 82 When cube is divided =   (114x+82)3/19 {(114x)3 + 3 x (114x) x 82 x (114x+82) + 823} /19 6x(114x)2 + (3 x 6x x 82 x (114x+82)) + 823 /19 Remainder will be left for 823 /19 (76+6)3 /19 = ( 762 + 3x 4 x 6 +( 63 /19) 216/19 = 19x11+7 Now, 
 = 7 remainder
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