SPOJ.com - Problem CPDUEL5A

CPDUEL5A - Comet Number

A positive integer X is a comet number if there exists 5 positive integers A B C D E such that:

A + B + C + D = X
A + E, B - E, C * E, and D / E are pairwise equal, meaning A + E = B - E = C * E = D / E

Kanata gave Suisei N positive integers A_i for 1 ≤ i ≤ N.

Suisei would like to know whether A_i is a comet number or not.

The first line contains an integer N.

The next N lines contain an integer A_i.

Print N lines.

The i-th line contains the string "YES" (without quotes) if A_i is a comet number and "NO" (without quotes) otherwise.

Input:
4
8
1
69
128

Output:
YES
NO
NO
YES

8 is a comet number as there exists a valid quintuple (A, B, C, D, E) = (1, 3, 2, 2, 1).

128 is a comet number as there exists a valid quintuple (A, B, C, D, E) = (31, 33, 32, 32, 1).

1 ≤ N, A_i ≤ 10⁵

Submit solution!



2021-08-27 06:55:41 Waseem Ahmed Thanks for the hints @@sachinverma and @robosapien
2021-01-02 19:47:33 Sachin verma Simple maths and loop. Also, might be obvious but watch out for the "positive integers" bit, costed me few WAs.
2020-11-26 20:16:08 nice problem.. just one observation does the job. :)
2020-11-09 08:54:44 Sushovan Sen @nadstratosfer please try to keep one successful submission per user. Otherwise it dilutes points gained for other users. It may not matter for you but it may matter for somebody else. [NG]: The points are calculated based on number of users who got AC, not the separate submissions. Speaking of dilluting the points though, I wonder how come the first AC here was achieved by a chinese bot from another judge system... Last edit: 2020-11-09 11:21:13
2020-11-08 17:17:18 1) Please replace Ai with X for simplicity and consistency. 2) Please explain what "A + E, B - E, C * E, and D / E are pairwise equal" means; assuming that A+E = B-E and C*E = D/E allows a quintuple (5, 9, 11, 44, 2) for X=69.