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diff --git a/Doc/Sd1/statements.xml b/Doc/Sd1/statements.xml
index 090a0984efd9f0efd10cf3ecd3a2ebee3282fad6..d70d1cc06dbcb6a9c7498aaa6549dd552d600828 100644
--- a/Doc/Sd1/statements.xml
+++ b/Doc/Sd1/statements.xml
@@ -2691,9 +2691,18 @@ import java.util.Random;
<qandadiv>
<qandaentry>
<question>
- <para>Read the <link
- xlink:href="https://en.wikipedia.org/wiki/Pythagorean_triple">definition
- of Pythagorean triples</link>.</para>
+ <para><link
+ xlink:href="https://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean
+ triples</link> are integer combinations of three values being
+ related by the <link
+ xlink:href="https://en.wikipedia.org/wiki/Pythagorean_theorem">Pythagorean
+ theorem</link>:</para>
+
+ <mediaobject>
+ <imageobject>
+ <imagedata fileref="Ref/Statements/phythagorean.svg"/>
+ </imageobject>
+ </mediaobject>
<para>Find all <link
xlink:href="https://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean
@@ -2741,8 +2750,7 @@ import java.util.Random;
</inlineequation>.</para>
<tip>
- <para>Think of writing a program which creates all possible
- triples <inlineequation>
+ <para>Think of creating all possible triples <inlineequation>
<m:math display="inline">
<m:mrow>
<m:mo>(</m:mo>
@@ -2807,7 +2815,8 @@ import java.util.Random;
</tr>
</informaltable>
- <para>Why does the value 998 appear here?</para>
+ <para>Why does a value of 838 rather then 840 appears
+ here?</para>
<para>This list mostly contains values like <inlineequation>
<m:math display="inline">
@@ -2819,60 +2828,68 @@ import java.util.Random;
<m:mo>,</m:mo>
- <m:mn>4</m:mn>
+ <m:mn>3</m:mn>
<m:mo>,</m:mo>
- <m:mn>3</m:mn>
+ <m:mn>4</m:mn>
</m:mrow>
<m:mo>)</m:mo>
</m:mrow>
</m:math>
- </inlineequation> failing to obey our restriction
+ </inlineequation> failing both our restrictions
<inlineequation>
<m:math display="inline">
<m:mrow>
<m:mrow>
- <m:mn>1</m:mn>
-
- <m:mo>+</m:mo>
+ <m:msup>
+ <m:mn>1</m:mn>
- <m:mn>4</m:mn>
+ <m:mn>2</m:mn>
+ </m:msup>
<m:mo>+</m:mo>
- <m:mn>3</m:mn>
+ <m:msup>
+ <m:mn>3</m:mn>
+
+ <m:mn>2</m:mn>
+ </m:msup>
</m:mrow>
<m:mo>≠</m:mo>
- <m:mi>840</m:mi>
+ <m:msup>
+ <m:mn>4</m:mn>
+
+ <m:mn>2</m:mn>
+ </m:msup>
</m:mrow>
</m:math>
- </inlineequation>. These triples have thus to be filtered
- retaining only the desired combinations simultaneously obeying
- both <inlineequation>
+ </inlineequation> and <inlineequation>
<m:math display="inline">
<m:mrow>
<m:mrow>
- <m:mi>a</m:mi>
+ <m:mn>1</m:mn>
<m:mo>+</m:mo>
- <m:mi>b</m:mi>
+ <m:mn>3</m:mn>
<m:mo>+</m:mo>
- <m:mi>c</m:mi>
+ <m:mn>4</m:mn>
</m:mrow>
- <m:mo>=</m:mo>
+ <m:mo>≠</m:mo>
<m:mi>840</m:mi>
</m:mrow>
</m:math>
- </inlineequation> and <inlineequation>
+ </inlineequation>. These triples have thus to be filtered
+ retaining only the desired combinations simultaneously obeying
+ both <inlineequation>
<m:math display="inline">
<m:mrow>
<m:mrow>
@@ -2900,6 +2917,26 @@ import java.util.Random;
</m:msup>
</m:mrow>
</m:math>
+ </inlineequation> and <inlineequation>
+ <m:math display="inline">
+ <m:mrow>
+ <m:mrow>
+ <m:mi>a</m:mi>
+
+ <m:mo>+</m:mo>
+
+ <m:mi>b</m:mi>
+
+ <m:mo>+</m:mo>
+
+ <m:mi>c</m:mi>
+ </m:mrow>
+
+ <m:mo>=</m:mo>
+
+ <m:mi>840</m:mi>
+ </m:mrow>
+ </m:math>
</inlineequation>. This might be accomplished by
implementing three nested loops:</para>