from research import *
s=begin(639,'Solve the two-calendar compatibility equation','What count family permits an Enochian corresponding span and a Priestly minimum fourteen years shorter?',{'equation':'182m−14=168n','positive_integer_counts':True},['Derived from File70 §6 source geometry'])
examples=[[1+12*q,1+13*q] for q in range(4)]
finish(s,{'reduced_equation':'13m−12n=1','general_solution':'m=1+12q; n=1+13q','examples_m_n':examples,'source_choice_q':1},'The pair of calendar requirements has an infinite integer family. Its source member is m=13,n=14; the smaller m=n=1 also fits the two-calendar equation. The exposure condition must supply any stronger selection.','Add the fixed thirteen-year exposure flanks and solve the complete three-calendar system.',{'examples':all(182*m-14==168*n for m,n in examples),'source_member':examples[1]==[13,14],'not_unique_pair':examples[0]==[1,1]})