Number Theory/Expert Profile

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Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience in the area

Teacher of math for 53 years


AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley


Journal of mathematics and its applications M500 magazine


BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors

State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients

I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

What do you like about this subject?

The variety, and the fact that everyone can participate. Anyone could discover a new largest prime number by joining the Mersenne prime project, using their computer off-line in the background to do masses of calculations.

What do you still hope to achieve/learn in this field?

I would love to have enough knowledge to completely understand Andrew Wiles's proof of Fermat's last theorem.

Something interesting about this subject that others may not know:

Secure encrypted messaging can be dependent on the difficulty of factorising the product of two large prime numbers.

Something controversial or provocative about this subject

Does the beauty I find in number theory demand a divine creator for the Universe?

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Recent Reviews from Users

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    K = Knowledgeability    C = Clarity of Response    P = Politeness
Prashant S Akerkar 03/23/17101010 
Prashant S Akerkar03/23/17101010Dear Prof Vijilant Thanks. Prashant
Prashant S Akerkar 03/23/17101010 
Prashant S Akerkar 03/23/17101010Dear Prof Vijilant Thanks. Prashant
Prashant S Akerkar 03/20/17101010Dear Prof Vijilant Thanks. Prashant

Recent Answers from Vijilant

2017-03-23 Compute Cross Sectional area of Solids.:

We can only talk about cross sectional area if it is the same everywhere.  i.e. The shape has to be a prism, for example a cuboid, a cylinder, a triangular prism.  None of the shapes you give are prisms

2017-03-12 Simple Harmonic Motion:

Hello Prashant  The answer is No.  Simple harmonic motion is where the acceleration of a point is proportional to its displacement from a fixed point and in the opposite direction.  This gives a second

2017-01-07 Joint Proportionality:

Hello Kenneth  I misunderstood your question.  It is the number of gallons that is the dependent variable which is directly proportional to the number of miles and to the number of trips.  g = kmt, so

2017-01-03 Joint Proportionality:

Hello Kenneth  I agree with your calculation of k.  But miles per gallon was not one of the variables.  Clearly if you increase the number of miles per gallon, you decrease gallons per trip, so these are

2016-12-04 Geometric Progression:

Hello Isabel  You are given that ABC is a straight line.  There are two similar triangles in the figure.  Calling the heights of the three, x,y and z, where x>y>z, then using the similar triangles gives


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