Hi,
First thankyou
chetan2u, you have given a wonderful ready to use result that would be very useful for lot of questions especially on divisibility.
If i may take liberty to repost the result that you have shared, if I were to remember ( actuality no need to memories since is understood the reasoning behind it ) this result it would be as follows
If we have a consecutive series of "n" odd or "n"even numbers , then one of them will be will be definitely divisible by odd numbers <=n.
Lets take an series of 5 consecutive odd numbers, then as per this one of them will be definitely divisible by odd numbers <=5 ( that means the one of the numbers will be definitely divisible by (3, 5)
say the series is 5 consecutive odd numbers
101, 103,105, 107,109 So we have 105 is divisible by 5& 3 and 109 is divisible by 3.
Lets take another series of 5 consecutive
even numbers, then as per this one of them will be definitely divisible by odd numbers <=5 ( that means the one of the numbers will be definitely divisible by (3, 5)
say we have 100,102,104,106,108, We do have 100 divisible by 5 and (102 & 108) divisible by 3
Now say we have series of 7 consecutive odd number then one of them will be definitely divisible by odd numbers <=7( that means the one of the numbers will be definitely divisible by (3, 5, 7)
say the series is
101, 103,105, 107,109 ,111, 113 So we have 105 is divisible by 7, 5& 3 and 109 is divisible by 3.
We can expand from this result and get many more results that we can use during exams.
Thanks to
chetan2u