There are two arithmetic series. There may be common terms between two sequences. We have to prove whether or not common terms between two series also form an arithmetic series. If yes what is first term and common difference of this series.
I formulated this problem while solving an algorithm design problem. Under this problem we have different base number systems (2, 3, .... 35). We are given m suffixes (s1, s2, s3,....,sm) expressed in base number systems (b1, b2, b3, .... , bm) respectively. We have to find minimum number which when expressed in bases (b1, b2, b3....,bm) has suffix string (s1,s2,s3,...sm) respectively. Alphabets used are (0,1,2....9, A,B,C,...,X,Y,Z).
For example, we have following three base-suffix pairs
5 22 (base 5 and suffix 22; a = 12,d = 25)
11 A2 (base 11 and suffix A2; a = 112,d = 121)
18 4 (base 18 and suffix 4; ; a = 4,d = 18)
In this case required output is 112 in decimal.
Numbers that satisfy base-suffix pair condition form an arithmetic series. So to find minimum number that satisfy all base-suffix pair conditions we have to find an arithmetic series whose terms are common to all arithmetic series. This is the origin of problem I stated before.