Let "f\\in\\mathbb Z[x],\\,\\,f=b_0+b_1x+\\dots" and "s\\in S"
"fs=a_0b_0+\\dots \\in \\mathbb Z[x]" and "5\\mid a_0'=a_0b_0"
Hence, "fs\\in S" and "S" is an ideal of "\\mathbb Z[x]"
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