Prove that 25^11-5^19 is divisible by 31

First get everything to have the same base of 5

25^11 - 5^19

(5^2)^11 - 5^19

5^(2*11) - 5^19

5^22 - 5^19

Now factor out the GCF 5^19 to get

5^22 - 5^19

5^(19+3) - 5^(19+0)

5^19*5^3 - 5^19*5^0

5^19(5^3 - 5^0)

5^19(125 - 1)

5^19*(124)

At this point, we factor the 124 into 31*4 to end up with this full factorization: 5^19*31*4

Therefore, 25^11 - 5^19 is equivalent to 5^19*31*4

Since 31 is a factor of the original expression, this means the original expression is divisible by 31.

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day

dalila is incorrect. the whisker on the left is very long, going all the way out to 5. the whisker goes from 5 to 30, so it has a spread of 25. the rest of the box plot values are closer together, so 5 is an outlier