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What is the remainder when 13^25+15^12+17^29 is divided by 10?
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22 Jul 2025, 00:51
22 Jul 2025, 00:51
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What is the remainder when \(13^{25}+15^{12}+17^{29}\) is divided by 10?
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Re: What is the remainder when 13^25+15^12+17^29 is divided by 10?
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25 Jul 2025, 00:46
25 Jul 2025, 00:46
1
all we need is the units digit for the answer
13^25 follows the pattern of 3^25 => 3 ,9 ,7 ,1 ,....
15^12 follows the pattern of 5^12 => 5 ,5 , ....
17^29 follows the pattern of 7^29 => 7, 9, 3, 1,.....
divide 25 by 4 , reminder is 1
so 13^25 has a number with 3 as it units digit
15^12 has its units digit as 5
divid2 29 by 4, reminder is 1
17^1 has its units digit as 7
3 + 5 + 7 = 15
divide 15 by 10, reminder is 5
the answer's 5
kudos is appreciated
13^25 follows the pattern of 3^25 => 3 ,9 ,7 ,1 ,....
15^12 follows the pattern of 5^12 => 5 ,5 , ....
17^29 follows the pattern of 7^29 => 7, 9, 3, 1,.....
divide 25 by 4 , reminder is 1
so 13^25 has a number with 3 as it units digit
15^12 has its units digit as 5
divid2 29 by 4, reminder is 1
17^1 has its units digit as 7
3 + 5 + 7 = 15
divide 15 by 10, reminder is 5
the answer's 5
kudos is appreciated
gmatclubot
Re: What is the remainder when 13^25+15^12+17^29 is divided by 10? [#permalink]
25 Jul 2025, 00:46
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