tellmesomething
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- TL;DR Summary
- I just made some random arithmetic progressions and i noticed that the lowest common multiple of the common difference of any two arithmetic progressions is equal to the common difference of an AP generated by the common terms present in both of the APs.
If i take any two APs
say a=1; d=5;
1,6,11,16,21,26,31,36,41,46,51......1+(n-1)5.
say a=2; d=3;
2,5,8,11,14,17,20,23,26,29,32,35,38,41......2+(n-1)3.
If i pick out the common terms here, I get an AP again o common difference 15.
11,26,41....11+(n-1)15
How can i prove that the common terms of any 2 APs will give me another AP and the lowest common multiple of their common differences will be the common difference of the new AP? Any hints?
say a=1; d=5;
1,6,11,16,21,26,31,36,41,46,51......1+(n-1)5.
say a=2; d=3;
2,5,8,11,14,17,20,23,26,29,32,35,38,41......2+(n-1)3.
If i pick out the common terms here, I get an AP again o common difference 15.
11,26,41....11+(n-1)15
How can i prove that the common terms of any 2 APs will give me another AP and the lowest common multiple of their common differences will be the common difference of the new AP? Any hints?