Which power of two divides 13^4 - 11^4 into an integer?
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answers:
Steve A say: 13^4 - 11^4 = (13^2 +11^2)(13^2 -11^2)
= (169 +121)(13 +11)(13 -11)
(290)(24)2)
(29*5*2)(3*2^3)(2)
2^5 is the highest power of 2 that divides it.
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Johnathan say: 13^4 - 11^4
= (13^2 + 11^2)(13^2 - 11^2)
= (169 + 121)(13 + 11)(13 - 11)
= (2 * 145)(2^3 * 3)(2)
= 2^5(145 * 3).
The largest power of 2 that 13^4 - 11^4 is divisible by is 5.
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az_lender say: (13^2 - 11^2)(13^2 + 11^2)
= (13 - 11)(13 + 11)(290).
This is divisible by 2*8*2 = 32 = 2^5.
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sepia say: 13^4 - 11^4
= (13^2 + 11^2)( 13 + 11)(13 - 11)
= 2^5 × 3 × 5 × 29
The fifth power of two divides 13^4 - 11^4 into an integer.
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ted s say: ( 13² - 11²) ( 13² + 11²)...both are even so 2² works.....13² - 11² = (13 + 11 )(13 - 11) are both even....so 2^3 works
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nbeky say: wrcegghw
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vicov say: fjchzzya
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dvfvv say: enqvkjjy
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wkjin say: fhfsyoon
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cxcja say: gcceoewk
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Steve A say: 13^4 - 11^4 = (13^2 +11^2)(13^2 -11^2)
= (169 +121)(13 +11)(13 -11)
(290)(24)2)
(29*5*2)(3*2^3)(2)
2^5 is the highest power of 2 that divides it.
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nbsale say: Let's see if we can do it without calculating it out, even tho that's easy enough to do.
Applying the difference of two square formula a couple of time, you get:
13^4 - 11^4 = (13^2 + 11^2)(13 - 11)(13 + 11)
Now I think we have to multiply those out to get
(169+121)(2)(24) = 290(2)(24)
You have
2|290 but not 4
2|2 but not 4
8|24 but not 16
So it's 2x2x8 = 2^5
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