3 to the Power of 1343Date: 07/22/2003 at 23:08:11 From: Gemma Subject: Find the last two digits of 3 to the power of 1343 Find the last two digits of 3 to the power of 1343. I have looked through your archives; however, I cannot find the pattern for the 2nd to last digit of the multiples of three, i.e., the pattern is 01,03,09,27,81,43,29,87,61,83,49,47,41,23,69,07,21,... It is clear the last digit is 1,3,9,7 but how do I work out the 2nd to last? Thanks, Gemma Date: 07/23/2003 at 00:53:35 From: Doctor Jaffee Subject: Re: Find the last two digits of 3 to the power of 1343 Hi Gemma, Here is my suggestion. You already figured out that the last digit must be 1,3,7, or 9. Can you figure out which one? Once you do, focus your attention on just those powers of 3 that end in the digit you found. You will discover that the preceding digit follows a very easy predictable pattern. Give it a try and if you want to check your solution with me or if you have difficulties or other questions write back to me and I'll try to help you some more. - Doctor Jaffee, The Math Forum http://mathforum.org/dr.math/ Date: 07/23/2003 at 01:12:43 From: Doctor Greenie Subject: Re: Find the last two digits of 3 to the power of 1343 Hi, Gemma - You stopped just too soon in your display of the pattern for the last two digits. If you take the pattern a few more steps you will have what you need to solve your problem. You might have seen that the pattern was going to repeat soon by looking at the patterns of next-to-last digits for each different last digit. For example, for successive entries in your pattern with last digit 1, the next-to-last digits are 0, 8, 6, 4, 2, .... I think you can finish the problem on your own. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/ Date: 07/24/2003 at 05:26:49 From: Gemma Subject: Thank you (Find the last two digits of 3 to the power of 1343) Hey thanks! I got it now. |
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