If #p# is prime and #a in NN# is such that #p | a^50# with #a= prod_k f_k^(alpha_k)#with #f_k# being the prime factors for #a#,
then
#a^50 = prod_k f_k^(50 alpha_k)# then if #p# is prime one of the #f_k# must be equal to #p# so #f_(k_0) = p# and #a^50# has a factor which is #f_(k_0)^(50 alpha_(k_0)) = p^(50alpha_(k_0))#