Arthur D. answered • 08/15/18

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if N leaves a remainder of 1 when divided by 2, then N+1 must be divisible by 2

if N leaves a remainder of 2 when divided by 3, then N+1 must be divisible by 3

if N leaves a remainder of 3 when divided by 4, then N+1 must be divisible by 4

if N leaves a remainder of 4 when divided by 5, then N+1 must be divisible by 5

so, N+1 must be a multiple of 2, 3, 4, and 5

eliminate the 2 because it is a factor of 4

N+1 must be a multiple of 3, 4, and 5

N+1 must be 3*4*5=60

therefore N must be 60-1=59 which is the least number satisfying the above conditions