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anushree01
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M35-02 18 Aug 2025, 18:44
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v good Question, I`m sure not many will be able to get it right at first
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CapedCrusader09
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M35-02 19 Nov 2025, 03:47
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I like the solution - it’s helpful.
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saepeducimus
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M35-02 08 Dec 2025, 03:36
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I like the solution - it’s helpful.
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totamofficiis
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M35-02 04 Mar 2026, 02:55
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I like the solution - it’s helpful.
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socialsloth
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M35-02 04 Jul 2026, 12:28
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This is a great question that’s helpful for learning and I like the solution - it’s helpful.
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avellanjc
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M35-02 29 Jul 2026, 13:11
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Factoring the negative sign [Most straight forward explanation]
Since the first element is smaller than the second, you must realize that the result will be negative.
To find the units digit of a negative result, you factor out the negative sign.
  • The expression 66^6 - 5^{55} becomes -(5^{55} - 66^6)
Now, you just subtract the units digits inside the parenthesis:
You are subtracting a number ending in 6 from a number ending in 5: (...5) - (...6). You cannot subtract 6 from 5, you borrow a 1 from the tens digit , making the 5 a 15. 15 - 6 = 9.

A quick shortcut for this is whenever the first term is smaller, to find the real UD of the subtraction, Invert the subtraction, and borrow if needed. 5^{55} - 66^6. 5 - 6. Yow borrow 1 for the 5 so it becomes 15-6=9 so UD=9

Regards,

Juan C. Avellan
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M35-02 17 Aug 2026, 05:52
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I like the solution - it’s helpful.
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