claim: In particular, PMOD alters the data from the Nimbus7 / ERB record from 1989 to 1991.
evidence: However, the two other versions make sense over a principal ideal domain R : it suffices to replace integer by element of the domain and Z { \displaystyle \mathbb { Z }  } by R. These two versions of the theorem are true in this context, because the proofs ( except for the first existence proof ), are based on Euclid's lemma and Bezout's identity, which are true over every principal domain.