A Mesmerising number theory problem
Number Theory
Level
pending
A positive integer decreases an integral number of times when its last digit is deleted. Find the total number of all such numbers.
The answer is 12.
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1 solution
Here, let n= 10^n.a +...+c+ k , a,...,k being integers. be a n digited no.
Now, 1 0 n . a + . . . + c 1 0 n . a + . . . + c + k = m , m being integer i.e. 1 0 n . a + . . . + c k is an integer.
Therefore, 10^n.a +...+c= 1 or a divisor of k.
Since k is a single digit, therefore n is double-digit no. and the solution is found after calculations.
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