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Abstract: For a prime p and nonnegative integers n,k, consider the set A {n,k}^{p}={xis in 0,1,

.,n: p^k||binom {n} {x}}. Let the expansion of n+1 in base p be:n+1=alpha {0} p^{ u}+alpha {1}p^{nu-1}+

.+alpha {nu}, where 0<=alpha {i}<=p-1,i=0,

.,nu. Then the number n is called a binomial predictor in base p,if|A {n,k}^{p}|=alpha {k}p^{nu-k},k=0,1,

.,nu. We give a full description ofthe binomial predictors in base p.

Author: Vladimir Shevelev



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