“…If 1 ^ /с g r, it follows that either a""i or a" does not belong to Ml^'^^. The Chinese Remainder Theorem guarantees beR such that b = = 0 {mod Ml^"-^) if а"_1фМ1''''\ b = ^modMf""^) if a"_^eMl^^\ for /c = = 1, 2,..., r. Hence a"_i + ba^ ф Ml'"'^^, к = 1,..., r, and if (a^,..., a"_2, «n-i + (For details, see [1], Lemma 3.3. )Since del,the induction hypothesis assures us of an (n -1) X (n -1) matrix D whose first row is a^, ..., a"_i + ba" and such that det D = d. и we let 71-2 [0 ... 0 1 then В is the desired matrix…”