I had posted earlier about some of the attributes of the number 7056 and 57767 and this is an extension of that
7056
a) 7056 is 84 x 84
b) Now check this sequence - 84, 70, 56 (This is the only 4 digit square which exhibits this sequence)
c) 70 ^ 2 - 56 ^ 2 = 1764 which is 42 x 42 and 42 is half of 84!
d) Also 42 extends the AP sequence highlighted in (b) = 84, 70, 56, 42!
e) Anagram of 42 is 24 and whose square is 576 (0576) which is anagram of 7056!
5776
a) 5776 is 76 x 76
b) Only 4 digit square (not ending with 25) whose last 2 digits are the original number itself
c) 57 - 19 x 3 and 76 - 19 x 4 and again one of the few squares which exhibit this sequence
d) Similar to 7056, 576 is again a subset of 5776 and a perfect square
e) Add 2000 to 5776 gives 7776 which is unique in its own sense - 3 ^ 5 x 2 ^ 5
Last but not the least - Prefix 1 to both 7056 and 5776
The resulting numbers are 17056 and 15776 and the similarities are striking
17056 - 2 ^ 5 x 13 x 41
15776 - 2 ^ 5 x 17 x 29
Both have 2 ^ 5 and a combination of 2 odd numbers as a factor
7056
a) 7056 is 84 x 84
b) Now check this sequence - 84, 70, 56 (This is the only 4 digit square which exhibits this sequence)
c) 70 ^ 2 - 56 ^ 2 = 1764 which is 42 x 42 and 42 is half of 84!
d) Also 42 extends the AP sequence highlighted in (b) = 84, 70, 56, 42!
e) Anagram of 42 is 24 and whose square is 576 (0576) which is anagram of 7056!
5776
a) 5776 is 76 x 76
b) Only 4 digit square (not ending with 25) whose last 2 digits are the original number itself
c) 57 - 19 x 3 and 76 - 19 x 4 and again one of the few squares which exhibit this sequence
d) Similar to 7056, 576 is again a subset of 5776 and a perfect square
e) Add 2000 to 5776 gives 7776 which is unique in its own sense - 3 ^ 5 x 2 ^ 5
Last but not the least - Prefix 1 to both 7056 and 5776
The resulting numbers are 17056 and 15776 and the similarities are striking
17056 - 2 ^ 5 x 13 x 41
15776 - 2 ^ 5 x 17 x 29
Both have 2 ^ 5 and a combination of 2 odd numbers as a factor
No comments:
Post a Comment