19657 Let x - 53651 = 9999 33994 Then, x = 9999 + 53651 = 63650 ----- 53651 -----
2079 is divisible by each of 3, 7, 9, 11.
Given Exp. = | (12)3 x 64 | = | (12)3 x 64 | = (12)2 x 62 = (72)2 = 5184 |
432 | 12 x 62 |
∴ x = 3, as 632 is divisible 8.
4 | x z = 6 x 1 + 4 = 10 ----------- 5 | y -2 y = 5 x z + 3 = 5 x 10 + 3 = 53 ----------- 6 | z - 3 x = 4 x y + 2 = 4 x 53 + 2 = 214 ----------- | 1 - 4 Hence, required number = 214.
Since 653xy is divisible by 2 and 5 both, so y = 0.
Now, 653x is divisible by 8, so 13x should be divisible by 8.
This happens when x = 6.
∴x + y = (6 + 0) = 6.
∴ x = 7.
Given Exp. | = (397)2 + (104)2 + 2 x 397 x 104 |
= (397 + 104)2 | |
= (501)2 = (500 + 1)2 | |
= (5002) + (1)2 + (2 x 500 x 1) | |
= 250000 + 1 + 1000 | |
= 251001 |
The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.
Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
∴Required value of * is 6.
1904 x 1904 | = (1904)2 |
= (1900 + 4)2 | |
= (1900)2 + (4)2 + (2 x 1900 x 4) | |
= 3610000 + 16 + 15200. | |
= 3625216. |
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