Consider a positive integer n=a1a2...ak, k≥2. A trunk of n is a number of the form a1a2...at, 1≤t≤k-1. (For example, the number 23 is a trunk of 2351)
By T(n) we denote the sum of all trunks of n and let S(n)=a1+a2+...+ak. Prove that n=S(n)+9T(n)
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