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443^443 what are the last three digits ?

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443^443 what are the last three digits ?

Guest Aug 29, 2014

#2
+26405
+5

Successive powers of 443 end in 443; 249; 307; 001.  These then repeat (see below).

The first of these occurs when mod(power,4) = 1, the second when mod(power,4) = 2, the third when mod(power,4) = 3 and the fourth when mod(power,4) = 0.

Since mod(443,4) = 3, the last three digits of 443443 are 307.

Alan  Aug 29, 2014
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#1
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AzizHusain  Aug 29, 2014
#2
+26405
+5

Successive powers of 443 end in 443; 249; 307; 001.  These then repeat (see below).

The first of these occurs when mod(power,4) = 1, the second when mod(power,4) = 2, the third when mod(power,4) = 3 and the fourth when mod(power,4) = 0.

Since mod(443,4) = 3, the last three digits of 443443 are 307.

Alan  Aug 29, 2014

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