What is the NO-SHORTCUT approach for learning great Mathematics?

# How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

Try this beautiful problem from Algebra PRMO 2019 based on Positive Integers.

## Positive Integers | PRMO | Problem 26

Positive integers x,y,z satisfy xy+z=160 compute smallest possible value of x+yz.

• 24
• 50
• 29
• 34

### Key Concepts

Algebra

Integer

sum

PRMO-2019, Problem 26

Higher Algebra by Hall and Knight

## Try with Hints

First hint

x+yz=$\frac{160-z}{y}$+yz

=$\frac{160}{y}+\frac{z(y^{2}-1)}{y}=\frac{160-z}{y}+\frac{zy^{2}}{y}=\frac{160-z}{y}+zy$

for particular value of z, $x+yz \geq 2\sqrt{z(160-z)}$

or, least value=$2\sqrt{z(160-z)}$ but an integer also

Second Hint

for least value z is also

case I z=1, $x+yz=\frac{159}{y}+y$ or, min value at y=3 which is 56

case II z=2, $x+yz=\frac{158}{y}+2y$ or, min value at y =2 which is 83 (not taken)

case III z=3, $x+yz=\frac{157}{y}+3y$ or, min value at y=1 which is 160 (not taken)

case IV z=4, $x+yz=\frac{156}{y}+4y$ or, min at y=6 which is 50 (taken)

Final Step

case V z=5, $x+yz=\frac{155}{y}+5y$ or, minimum value at y=5 which is 56 (not taken)

case VI z=6, $x+yz=\frac{154}{y}+6y$ $\geq 2\sqrt{924}$>50

smallest possible value =50.

## What to do to shape your Career in Mathematics after 12th?

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:

• What are some of the best colleges for Mathematics that you can aim to apply for after high school?
• How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
• What are the best universities for MS, MMath, and Ph.D. Programs in India?
• What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
• How can you pursue a Ph.D. in Mathematics outside India?
• What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

## Want to Explore Advanced Mathematics at Cheenta?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

To Explore and Experience Advanced Mathematics at Cheenta

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