Try this beautiful problem from the PRMO II, 2019 based on Sum of Digits base 10.
Let s(n) denote the sum of the digits of a positive integer n in base 10. If s(m)=20 and s(33m)=120, what is the value of s(3m)?
But try the problem first...
Answer: is 60.
PRMO II, 2019, Question 7
Elementary Algebra by Hall and Knight
taking sum of digit base 10 to (mod 9)
and s(ab)=s(a).s(b)(mod 9)
[ let x congruent r mod n, y congruent to s mod n,
\(0 \leq r,s \leq n-1\),
x=in+r, y=jn+s, i,j are integers
xy=(in+r)(jn+s)=ij\(n^2\)+(is+jr)n+rs congruent to rs mod n
so, xy mod n =(x mod n)(y mod n) ]
s(33m)=120=\(s(11) \times s(3m)\)
or, 120=\(2 \times s(3m)\) [ since s(11)=2(mod 9)]
From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here: