Find the least positive integer x satisfying: -
276 x+128  4(mod 7)
[Hint : 276   3, 128  2 (mod 7)]
 

Dear Student,
Please find below the solution to the asked query:

We have276x+1284mod 7276x+128-4 is a multiple of 7276x+124 is a multiple of 7276x+119+5 is a multiple of 7276x+5+7×17 is a multiple of 7As 7×17 is a multiple of 7276x+5  is a multiple of 7273+3x+5 is a multiple of 73x+5+273 is a multiple of 7As 273  is also a multiple of 73x+5 is a multiple of 7By hit and trial, least positive integer is x=3as 3×3+5=14 which is divisible of 7Hence x=3 Answer

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