When least becomes large enough?!!
Number Theory
Level
pending
Find the least number whose last digit is 7 and which becomes 5 times larger when this last digit is carried to the beginning of the number.
The answer is 142857.
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1 solution
Let the required number be ...abc7. Since it is given that 5(...abc7) = 7...abc we find that c=5. Putting this value of c back in the equation we have 5(...ab57) = 7...ab5 we find that b = 8. Continuing this way till we get 7 for the first place, we find that the required number is 142857.