| Author | Comment |
sith_lord501
Probe
Posted: 18 Oct 2006
17:48 GMT
Total Posts: 12 | ok i was helping my sister with extra credit and i got stuck on one of the questions can any one help and can you tell me how you got it?
Whats is the remainder when 7^348 + 25^605 id divided by 8?
pls help me |
Lunchbox
Carrier
Posted: 18 Oct 2006
20:29 GMT
Total Posts: 2007 | Ummm, that's a problem you'd need a TI-89 for, as it aactually will compute powers that high for you. But I don't see how that's feasible by hand. Are you sure those are powers and not multiplication signs? |
Liebe ist Krieg
Wraith
Posted: 18 Oct 2006
22:58 GMT
Total Posts: 542 | no... i see where they are going with that one... it involves the rules of powers, which is why the powers are so high, inorder to assure that it will be done by hand using the rules... which i dont remember.
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~~~~LiK~~~~ |
Lunchbox
Carrier
Posted: 19 Oct 2006
16:14 GMT
Total Posts: 2007 | Ahhh, yes. I see what you mean. In that case, you should simplify it to (7^348 + 5^1210) / 8 and find the first three digits, as they are the only ones that matter in terms of dividing by eight. And, for that matter, the last three digits of the 5 power are 625. 7, however, is trickier. The first digit cycles through the order 7, 9, 3, 1 repeatingly, resulting in a 1 in your situation. The second digit alternates between 4 and 0, with each getting two iterations before switching, given that the first power of seven has no second digit, therefore it produces a 0 when the power is 348. The third and final digit you need to know goes according to the pattern odd, even, even, even starting with 7^3 and repeating infinitely thereafter. And with that, we can dedude that the third digit of the combined answer is even (even + even = even), and the last two digits are 2 and 6, respectively. And thus, we produce the answer of 2, because *26 % 8 (% means modulus, a function in most programming languages which just gets the remainder of the division) when * is even is always 2, see 26, 226, and 426 as examples.
Did that help? :D |
Zachary940
Wraith
Posted: 19 Oct 2006
17:22 GMT
Total Posts: 714 | This is wht TI invented calculators
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It is much easier to suggest solutions when you know nothing about the problem. |
Lunchbox
Carrier
Posted: 19 Oct 2006
18:29 GMT
Total Posts: 2007 | That's called original thinking, something there is a dismal lack of in this world today. |
Liebe ist Krieg
Wraith
Posted: 20 Oct 2006
11:40 GMT
Total Posts: 542 | caclulators cant compute that equation, other wise i would've done it.
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~~~~LiK~~~~ |
ryantmer
Wraith
Posted: 20 Oct 2006
20:28 GMT
Total Posts: 692 | Some calculators can. |
sky euphoria
Probe
Posted: 21 Oct 2006
01:14 GMT
Total Posts: 7 | yep |
Lunchbox
Carrier
Posted: 21 Oct 2006
11:06 GMT
Total Posts: 2007 | TI-89 can, thus the reason I said you should use one of those. |
