Online Course Discussion Forum

1.12, 1.13, 1.15, 1.16

 
 
Picture of Tina Jin
1.12, 1.13, 1.15, 1.16
by Tina Jin - Saturday, 13 May 2023, 4:22 PM
 

Hello!


I am stuck on these problems: 1.12, 1.13, 1.15, 1.16


Can I get some hints?


Thanks!


Tina Jin

 
Picture of Dr. Kevin Wang
Re: 1.12, 1.13, 1.15, 1.16
by Dr. Kevin Wang - Saturday, 27 May 2023, 12:38 AM
 

1.12: this is the sum $1200^3 + 1^3$.

1.13: You can assume $a\geq b\geq c$ without loss of generality.

1.15: The last digit is $2$.  If you multiply this number by $2$, the last digit $2$ is moved to the first digit.  With this information, you can simply carry out the multiplication on paper, until the first digit of the result is $2$.  This number has more than 10 digits.

1.16: Consider pairing and symmetry.